# 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:
 [1] F. Autieri, N. Parolini and L. Quartapelle, Numerical investigation on the stability of singular driven cavity flow, J. Comput Phys, 183 (2002), 1-25. doi: 10.1006/jcph.2002.7145. [2] S. Badia, A. Quaini and A. Quarteroni, Modular vs. non-modular preconditioners for fluid-structure systems with large added-mass effect, Comput. Methods Appl. Mech. Engrg., 197 (2008), 4216-4232. doi: 10.1016/j.cma.2008.04.018. [3] S. Badia, A. Quaini and A. Quarteroni, Splitting methods based on algebraic factorization for fluid-structure interaction, SIAM J. Sci. Comput., 30 (2008), 1778-1805. doi: 10.1137/070680497. [4] S. Badia, A. Quaini and A. Quarteroni, Coupling Biot and Navier-Stokes equations for modelling fluid-poroelstic media interaction, J. Comput. Phys., 228 (2009), 7986-8014. 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), 1201-1210. doi: 10.1002/fld.796. [6] F. Brezzi and M. Fortin, "Mixed and Hybrid Finite Element Methods," Springer Series in Computational Mathematics, 15, Springer-Verlag, New York, 1991. [7] J. Coats, "A Manual Of Pathology," Longmans, Green, and Co., 1999. [8] R. Codina, Stabilized finite element approximation of transient incompressible flows using orthogonal subscales, Comput. Methods Appl. Mech. Engrg., 191 (2002), 4295-4321. doi: 10.1016/S0045-7825(02)00337-7. [9] A. Cordero, S. Castaño and G. Rábago, Prosthetic aortic valve thrombosis after Left Ventricular Assist Device implantation, Rev. Esp. Cardiol., 58 (2005), 863. [10] J. A. Crestanelloa, D. A. Orsinellib, M. S. Firstenberga and C. Sai-Sudhakar, Aortic valve thrombosis after implantation of temporary Left Ventricular Assist Device, Interactive Cardiovascular and Thoracic Surgery, 8 (2009), 661-662. doi: 10.1510/icvts.2009.202242. [11] L. Formaggia and F. Nobile, A stability analysis for the arbitrary Lagrangian Eulerian formulation with finite elements, East-West J. Num. Math., 7 (1999), 105-131. [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., in press, 2010. doi: 10.1097/MAT.0b013e3181d861f1. [13] M. A. Gimbrone, Endothelial disfunction, hemodynamic forces, and atherosclerosis (pubmed abstract), Thrombos Haemost, 82 (1999), 722-726. [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 outflow-graft placement on hemodynamics and flow: Implantation technique and computer flow modeling, Texas Heart Institute Journal, 32 (2005), 294-298. [15] K. D. May-Newman, 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), 105-109. 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), 203-204. [17] F. Nobile, "Numerical Approximation of Fluid-Structure Interaction Problems with Application to Haemodynamics," Ph.D thesis, École Polytechnique Fédérale de Lausanne, 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, Springer-Verlag, Berlin, 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 sub-aortic thrombosis in 2 patients with aortic valve bioprosthesis, Journal of Heart and Lung Transplantation, 22 (2003), 594-599. doi: 10.1016/S1053-2498(02)01180-4. [21] Y. Saad, "Iterative Methods for Sparse Linear Systems," 2nd edition, Society for Industrial and Applied Mathematics, Philadelphia, PA, 2003. [22] D. Seiffge, Thrombotic reactions of vascular anastomoses: Comparison of model studies with experimental findings, Vasa Suppl., 32 (1991), 54-56. [23] N. G. Smedira, Invited commentary: Valve disease and LVAD, Annals of Thoracic Surgery, 71 (2001), 1453. doi: 10.1016/S0003-4975(01)02577-2.

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), 1-25. doi: 10.1006/jcph.2002.7145. [2] S. Badia, A. Quaini and A. Quarteroni, Modular vs. non-modular preconditioners for fluid-structure systems with large added-mass effect, Comput. Methods Appl. Mech. Engrg., 197 (2008), 4216-4232. doi: 10.1016/j.cma.2008.04.018. [3] S. Badia, A. Quaini and A. Quarteroni, Splitting methods based on algebraic factorization for fluid-structure interaction, SIAM J. Sci. Comput., 30 (2008), 1778-1805. doi: 10.1137/070680497. [4] S. Badia, A. Quaini and A. Quarteroni, Coupling Biot and Navier-Stokes equations for modelling fluid-poroelstic media interaction, J. Comput. Phys., 228 (2009), 7986-8014. 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), 1201-1210. doi: 10.1002/fld.796. [6] F. Brezzi and M. Fortin, "Mixed and Hybrid Finite Element Methods," Springer Series in Computational Mathematics, 15, Springer-Verlag, New York, 1991. [7] J. Coats, "A Manual Of Pathology," Longmans, Green, and Co., 1999. [8] R. Codina, Stabilized finite element approximation of transient incompressible flows using orthogonal subscales, Comput. Methods Appl. Mech. Engrg., 191 (2002), 4295-4321. doi: 10.1016/S0045-7825(02)00337-7. [9] A. Cordero, S. Castaño and G. Rábago, Prosthetic aortic valve thrombosis after Left Ventricular Assist Device implantation, Rev. Esp. Cardiol., 58 (2005), 863. [10] J. A. Crestanelloa, D. A. Orsinellib, M. S. Firstenberga and C. Sai-Sudhakar, Aortic valve thrombosis after implantation of temporary Left Ventricular Assist Device, Interactive Cardiovascular and Thoracic Surgery, 8 (2009), 661-662. doi: 10.1510/icvts.2009.202242. [11] L. Formaggia and F. Nobile, A stability analysis for the arbitrary Lagrangian Eulerian formulation with finite elements, East-West J. Num. Math., 7 (1999), 105-131. [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., in press, 2010. doi: 10.1097/MAT.0b013e3181d861f1. [13] M. A. Gimbrone, Endothelial disfunction, hemodynamic forces, and atherosclerosis (pubmed abstract), Thrombos Haemost, 82 (1999), 722-726. [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 outflow-graft placement on hemodynamics and flow: Implantation technique and computer flow modeling, Texas Heart Institute Journal, 32 (2005), 294-298. [15] K. D. May-Newman, 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), 105-109. 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), 203-204. [17] F. Nobile, "Numerical Approximation of Fluid-Structure Interaction Problems with Application to Haemodynamics," Ph.D thesis, École Polytechnique Fédérale de Lausanne, 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, Springer-Verlag, Berlin, 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 sub-aortic thrombosis in 2 patients with aortic valve bioprosthesis, Journal of Heart and Lung Transplantation, 22 (2003), 594-599. doi: 10.1016/S1053-2498(02)01180-4. [21] Y. Saad, "Iterative Methods for Sparse Linear Systems," 2nd edition, Society for Industrial and Applied Mathematics, Philadelphia, PA, 2003. [22] D. Seiffge, Thrombotic reactions of vascular anastomoses: Comparison of model studies with experimental findings, Vasa Suppl., 32 (1991), 54-56. [23] N. G. Smedira, Invited commentary: Valve disease and LVAD, Annals of Thoracic Surgery, 71 (2001), 1453. doi: 10.1016/S0003-4975(01)02577-2.
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