Warning about the Risk of Blood Flow Stagnation after Transcatheter Aortic Valve Implantation
In this work, the hemodynamics in the sinuses of
Valsalva after Transcatheter Aortic Valve Implantation is numerically
examined. We focus on the physical results in the two-dimensional
case. We use a finite element methodology based on a Lagrange
multiplier technique that enables to couple the dynamics of blood
flow and the leaflets’ movement. A massively parallel implementation
of a monolithic and fully implicit solver allows more accuracy and
significant computational savings. The elastic properties of the aortic
valve are disregarded, and the numerical computations are performed
under physiologically correct pressure loads. Computational results
depict that blood flow may be subject to stagnation in the lower
domain of the sinuses of Valsalva after Transcatheter Aortic Valve
Implantation.
[1] P. R. Amestoy and I. S. Duff and J. Koster and J.-Y. L’Excellent,
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic
Scheduling, SIAM J. Matrix Anal. Appl., 2001, 23(1):15-41.
[2] M. Astorino, J. Hamers, S. C. Shadden and J.-F. Gerbeau, A robust
and efficient valve model based on resistive immersed surfaces, Int. J.
Numer. Methods Biomed. Engrg. 28(9):937–959 (2012).
[3] D. S. Bach, Prevalence and Characteristics of Unoperated Patients with
Severe Aortic Stenosis, J. Heart Valve Dis. 2011;20:284-291.
[4] S. Chandra, N. M. Rajamannan and P. Sucosky, Computational
assessment of bicuspid aortic valve wall-shear stress: implications
for calcific aortic valve disease, J. Biomechanics and Modeling in
Mechanobiology 2012, 11(7):1085-1096.
[5] E. De Marchena, J. Mesa, S. Pomenti, C. M. Kall, X. Marincic, K.
Yahagi, E. Ladich, R. Kutys, Y. Aga, M. Ragosta, A. Chawla, M. E.
Ring and R. Virmani, Thrombus Formation Following Transcatheter
Aortic Valve Replacement, JACC: Cardiovascular Interventions 2015,
8(5):728-739
[6] R. V. Freeman and C. M. Otto, Spectrum of calcific aortic valve disease.
Pathogenesis, disease progression and treatment strategies, Circulation.
2015, 111:3316-3326.
[7] C. Geuzaine and J.-F. Remacle, Gmsh: A 3-D finite element mesh
generator with built-in pre- and post-processing facilities, Int. J. Numer.
Meth. Engng., 2009, 79: 1309-1331.
[8] T. Korakianitis and Y. Shi, A concentrated parameter model for the
human cardiovascular system including heart valve dynamics and
atrioventricular interaction, Med. Eng. Phys. 2006, 28(7):613-628.
[9] A. Laadhari and G. Sz´ekely, Eulerian finite element method for the
numerical modeling of fluid dynamics of natural and pathological aortic
valves, J. Comput. Appl. Math. (submitted 2016).
[10] A. Laadhari, A. Quarteroni, Numerical modeling of heart valves using
resistive Eulerian surfaces, Int. J. Numer. Method. Biomed. Eng. 32(5)
(2016).
[11] A. Laadhari, P. Saramito, C. Misbah, An adaptive finite element method
for the modeling of the equilibrium of red blood cells, Int. J. Numer.
Meth. Fluids 80 (2016) 397–428.
[12] A. Laadhari, P. Saramito and C. Misbah, Computing the dynamics of
biomembranes by combining conservative level set and adaptive finite
element methods, J. Comput. Phys. 263 (2014) 328–352.
[13] J. K-J. Li, Laminar and turbulent flow in the mammalian aorta: Reynolds
number, Journal of Theoretical Biology (1988), 135(3):409–414.
[14] M. Lindroos, M. Kupari, J. Heikkil¨a, R. Tilvis, Prevalence of aortic valve
abnormalities in the elderly: an echocardiographic study of a random
population sample, J. Am. Coll. Cardiol. 1993;21(5):1220-1225.
[15] S. N. Miandoab and R. E. Michler, A Review of Most Relevant
Complications of Transcatheter Aortic Valve Implantation, ISRN
Cardiology 2013;12:2013.
[16] M.P.I. Forum, MPI: A Message-Passing Interface Standard, http://www.
mpi-forum.org (Accessed: 28.11.2016).
[17] MUMPS: MUltifrontal Massively Parallel Solver, http://mumps.
enseeiht.fr/index.php (Accessed: 28.11.2016).
[18] J. D. Newton, S. Redwood and B. D. Prendergast, Transcatheter aortic
valve implantation: a durable treatment option in aortic stenosis?, Heart
2015, 101(12):913-914.
[19] C. M. Otto, J. Knuusisto, D. D. Reichenbach, A. M. Gown and K.
D. O’Brien, Characterization of the early lesion of ”degenerative”
valvular aortic stenosis. Histological and immunohistochemical studies,
Circulation. 1994;90(2):844-853.
[20] Paraview: Parallel visualization application, http://paraview.org
(Accessed: 28.11.2016).
[21] P. Saramito, Efficient C++ finite element computing with Rheolef,
CNRS-CCSD ed., 2013. http://www-ljk.imag.fr/membres/Pierre.
Saramito/rheolef/rheolef-refman.pdf (Accessed: 22.09.16).
[22] K. S. Sakariassen, S. R. Hanson and Y. Cadroy, Methods and
models to evaluate shear-dependent and surface reactivity-dependent
antithrombotic efficacy, Thromb Res. 2001; 104: 149-174.
[23] J. M. Sinning, M. Vasa-Nicotera, D. Chin, C. Hammerstingl, A. Ghanem,
J. Bence, J. Kovac, E. Grube, G. Nickenig and N. Werner Evaluation
and management of paravalvular aortic regurgitation after transcatheter
aortic valve replacement, J. Am. Coll. Cardiol. 2013,62:11-20.
[24] B. A. Towfiq, J. Weir and J.M. Rawles, Effect of age and blood pressure
on aortic size and stroke distance, British Heart J. 1986, 55(6):560-568.
[25] N. Westerhof, G. Elzinga and P. Sipkema, An artificial arterial system
for pumping hearts, J. Appl. Physiol. 1971, 31(5), 776-781.
[26] H. J. Weiss, V. T. Turitto and H. R. Baumgartner, Role of shear rate
and platelets in promoting fibrin formation on rabbit subendothelium
- studies utilizing patients with quantitative and qualitative platelet
defects, J. Clin. Invest. 1986; 78: 1072-1082.
[27] T. Williams and C. Kelley, Gnuplot: An Interactive Plotting Program
http://www.gnuplot.info (Accessed: 28.11.2016).
[28] Y. R. Woo and A. P. Yogananthan, In vitro pulsatile flow velocity and
shear stress measurements in the vicinity of mechanical mitral heart
prostheses, J. Biomech. 1986;19:39-51.
[1] P. R. Amestoy and I. S. Duff and J. Koster and J.-Y. L’Excellent,
A Fully Asynchronous Multifrontal Solver Using Distributed Dynamic
Scheduling, SIAM J. Matrix Anal. Appl., 2001, 23(1):15-41.
[2] M. Astorino, J. Hamers, S. C. Shadden and J.-F. Gerbeau, A robust
and efficient valve model based on resistive immersed surfaces, Int. J.
Numer. Methods Biomed. Engrg. 28(9):937–959 (2012).
[3] D. S. Bach, Prevalence and Characteristics of Unoperated Patients with
Severe Aortic Stenosis, J. Heart Valve Dis. 2011;20:284-291.
[4] S. Chandra, N. M. Rajamannan and P. Sucosky, Computational
assessment of bicuspid aortic valve wall-shear stress: implications
for calcific aortic valve disease, J. Biomechanics and Modeling in
Mechanobiology 2012, 11(7):1085-1096.
[5] E. De Marchena, J. Mesa, S. Pomenti, C. M. Kall, X. Marincic, K.
Yahagi, E. Ladich, R. Kutys, Y. Aga, M. Ragosta, A. Chawla, M. E.
Ring and R. Virmani, Thrombus Formation Following Transcatheter
Aortic Valve Replacement, JACC: Cardiovascular Interventions 2015,
8(5):728-739
[6] R. V. Freeman and C. M. Otto, Spectrum of calcific aortic valve disease.
Pathogenesis, disease progression and treatment strategies, Circulation.
2015, 111:3316-3326.
[7] C. Geuzaine and J.-F. Remacle, Gmsh: A 3-D finite element mesh
generator with built-in pre- and post-processing facilities, Int. J. Numer.
Meth. Engng., 2009, 79: 1309-1331.
[8] T. Korakianitis and Y. Shi, A concentrated parameter model for the
human cardiovascular system including heart valve dynamics and
atrioventricular interaction, Med. Eng. Phys. 2006, 28(7):613-628.
[9] A. Laadhari and G. Sz´ekely, Eulerian finite element method for the
numerical modeling of fluid dynamics of natural and pathological aortic
valves, J. Comput. Appl. Math. (submitted 2016).
[10] A. Laadhari, A. Quarteroni, Numerical modeling of heart valves using
resistive Eulerian surfaces, Int. J. Numer. Method. Biomed. Eng. 32(5)
(2016).
[11] A. Laadhari, P. Saramito, C. Misbah, An adaptive finite element method
for the modeling of the equilibrium of red blood cells, Int. J. Numer.
Meth. Fluids 80 (2016) 397–428.
[12] A. Laadhari, P. Saramito and C. Misbah, Computing the dynamics of
biomembranes by combining conservative level set and adaptive finite
element methods, J. Comput. Phys. 263 (2014) 328–352.
[13] J. K-J. Li, Laminar and turbulent flow in the mammalian aorta: Reynolds
number, Journal of Theoretical Biology (1988), 135(3):409–414.
[14] M. Lindroos, M. Kupari, J. Heikkil¨a, R. Tilvis, Prevalence of aortic valve
abnormalities in the elderly: an echocardiographic study of a random
population sample, J. Am. Coll. Cardiol. 1993;21(5):1220-1225.
[15] S. N. Miandoab and R. E. Michler, A Review of Most Relevant
Complications of Transcatheter Aortic Valve Implantation, ISRN
Cardiology 2013;12:2013.
[16] M.P.I. Forum, MPI: A Message-Passing Interface Standard, http://www.
mpi-forum.org (Accessed: 28.11.2016).
[17] MUMPS: MUltifrontal Massively Parallel Solver, http://mumps.
enseeiht.fr/index.php (Accessed: 28.11.2016).
[18] J. D. Newton, S. Redwood and B. D. Prendergast, Transcatheter aortic
valve implantation: a durable treatment option in aortic stenosis?, Heart
2015, 101(12):913-914.
[19] C. M. Otto, J. Knuusisto, D. D. Reichenbach, A. M. Gown and K.
D. O’Brien, Characterization of the early lesion of ”degenerative”
valvular aortic stenosis. Histological and immunohistochemical studies,
Circulation. 1994;90(2):844-853.
[20] Paraview: Parallel visualization application, http://paraview.org
(Accessed: 28.11.2016).
[21] P. Saramito, Efficient C++ finite element computing with Rheolef,
CNRS-CCSD ed., 2013. http://www-ljk.imag.fr/membres/Pierre.
Saramito/rheolef/rheolef-refman.pdf (Accessed: 22.09.16).
[22] K. S. Sakariassen, S. R. Hanson and Y. Cadroy, Methods and
models to evaluate shear-dependent and surface reactivity-dependent
antithrombotic efficacy, Thromb Res. 2001; 104: 149-174.
[23] J. M. Sinning, M. Vasa-Nicotera, D. Chin, C. Hammerstingl, A. Ghanem,
J. Bence, J. Kovac, E. Grube, G. Nickenig and N. Werner Evaluation
and management of paravalvular aortic regurgitation after transcatheter
aortic valve replacement, J. Am. Coll. Cardiol. 2013,62:11-20.
[24] B. A. Towfiq, J. Weir and J.M. Rawles, Effect of age and blood pressure
on aortic size and stroke distance, British Heart J. 1986, 55(6):560-568.
[25] N. Westerhof, G. Elzinga and P. Sipkema, An artificial arterial system
for pumping hearts, J. Appl. Physiol. 1971, 31(5), 776-781.
[26] H. J. Weiss, V. T. Turitto and H. R. Baumgartner, Role of shear rate
and platelets in promoting fibrin formation on rabbit subendothelium
- studies utilizing patients with quantitative and qualitative platelet
defects, J. Clin. Invest. 1986; 78: 1072-1082.
[27] T. Williams and C. Kelley, Gnuplot: An Interactive Plotting Program
http://www.gnuplot.info (Accessed: 28.11.2016).
[28] Y. R. Woo and A. P. Yogananthan, In vitro pulsatile flow velocity and
shear stress measurements in the vicinity of mechanical mitral heart
prostheses, J. Biomech. 1986;19:39-51.
@article{"International Journal of Engineering, Mathematical and Physical Sciences:74822", author = "Aymen Laadhari and Gábor Székely", title = "Warning about the Risk of Blood Flow Stagnation after Transcatheter Aortic Valve Implantation", abstract = "In this work, the hemodynamics in the sinuses of
Valsalva after Transcatheter Aortic Valve Implantation is numerically
examined. We focus on the physical results in the two-dimensional
case. We use a finite element methodology based on a Lagrange
multiplier technique that enables to couple the dynamics of blood
flow and the leaflets’ movement. A massively parallel implementation
of a monolithic and fully implicit solver allows more accuracy and
significant computational savings. The elastic properties of the aortic
valve are disregarded, and the numerical computations are performed
under physiologically correct pressure loads. Computational results
depict that blood flow may be subject to stagnation in the lower
domain of the sinuses of Valsalva after Transcatheter Aortic Valve
Implantation.
", keywords = "Hemodynamics, Transcatheter Aortic Valve
Implantation, blood flow stagnation, numerical simulations.", volume = "11", number = "1", pages = "33-5", }
