Abstract
Cardiovascular diseases are still the leading causes of death in the developed world. The decline in the mortality associated with circulatory system diseases is accredited to development of new diagnostic and prognostic tools. It is well known that there is an inter relationship between the aortic valve impairment and pathologies of the aorta and coronary vessels. However, due to the limitations of the current tools, the possible link is not fully elucidated. Following our previous model of the aortic root including the coronaries, in this study, we have further developed the global aspect of the model by incorporating the anatomical structure of the thoracic aorta. This model is different from all the previous studies in the sense that inclusion of the coronary structures and thoracic aorta into the natural aortic valve introduces the notion of globality into the model enabling us to explore the possible link between the regional pathologies. The developed model was first validated using the available data in the literature under physiological conditions. Then, to provide a support for the possible association between the localized cardiovascular pathologies and global variations in hemodynamic conditions, we simulated the model for two pathological conditions including moderate and severe aortic valve stenoses. The findings revealed that malformations of the aortic valve are associated with development of low wall shear stress regions and helical blood flow in thoracic aorta that are considered major contributors to aortic pathologies.
Similar content being viewed by others
Abbreviations
- ALE:
-
Arbitrary Lagrangian–Eulerian
- AVA:
-
Aortic valve area
- BCa:
-
Brachiocephalic artery
- CB:
-
Conus branch
- CS:
-
Cross section
- DCx:
-
Distal circumflex
- DLAD:
-
Diagonal branch of the LAD
- ET:
-
Ejection time
- FD:
-
Fictitious domain
- FR:
-
Fiber reinforced
- FSI:
-
Fluid–solid interaction
- H:
-
Hyperplastic (nonlinear) material properties
- I:
-
Isotropic material properties
- L:
-
Linear material properties
- LAD:
-
Left anterior descending
- LCa:
-
Left carotid artery
- LCA:
-
Left coronary arteries
- LMS:
-
Left main stem
- LSa:
-
Left subclavian
- LVOT:
-
Left ventricle outflow tract
- MCx:
-
Main circumflex
- MLAD:
-
Main left anterior descending
- NA:
-
Not available
- O:
-
Orthotropic material properties
- OM:
-
Obtuse marginal
- PD:
-
Posterior descending
- R:
-
Rigid
- RCA:
-
Right coronary arteries
- RMS:
-
Right main stem
- RV:
-
Right ventricular
- RVCT:
-
Rapid valve closing time
- RVCV:
-
Rapid valve closing velocity
- RVOT:
-
Rapid valve opening time
- RVOV:
-
Rapid valve opening velocity
- STJ:
-
Sinotubular junction
References
Achilles J, Pappano WGW (2012) Cardiovascular physiology: Mosby physiology monograph series, 10th edn. Elsevier Health Sciences, Philadelphia
Ahmadi N et al (2011) Impaired aortic distensibility measured by computed tomography is associated with the severity of coronary artery disease. Int J Cardiovasc Imaging 27:459–469. doi:10.1007/s10554-010-9680-6
Astorino M, Gerbeau J-F, Pantz O, Traoré K-F (2009) Fluid-structure interaction and multi-body contact: application to aortic valves. Comput Method Appl Mech Eng 198:3603–3612. doi:10.1016/j.cma.2008.09.012
Aybek T et al (2005) Valve opening and closing dynamics after different aortic valve-sparing operations. J Heart Valve Dis 14:114–120
Azadani AN et al (2012) Biomechanical comparison of human pulmonary and aortic roots. Eur J Cardiothorac Surg 41:1111–1116. doi:10.1093/ejcts/ezr163
Badia S, Nobile F, Vergara C (2008) Fluid-structure partitioned procedures based on Robin transmission conditions. J Comput Phys 227:7027–7051
Basciano CA, Kleinstreuer C (2009) Invariant-based anisotropic constitutive models of the healthy and aneurysmal abdominal aortic wall. J Biomech Eng 131:021009. doi:10.1115/1.3005341
Berg HVD (2011) Mathematical models of biological systems. Oxford University Press, Oxford, New York
Berger S (1996) Introduction to bioengineering. Oxford University Press, Oxford, New York
Berger S, Talbot L, Yao L (1983) Flow in curved pipes. Annu Rev Fluid Mech 15:461–512
Billiar KL, Sacks MS (2000) Biaxial mechanical properties of the natural and glutaraldehyde treated aortic valve cusp-part I: experimental results. J Biomech Eng 122:23–30
Bissell MM et al (2013) Aortic dilation in bicuspid aortic valve disease: flow pattern is a major contributor and differs with valve fusion type. Circ Cardiovasc Imaging 6:499–507. doi:10.1161/circimaging.113.000528
Black MM, Howard IC, Huang X, Patterson EA (1991) A three-dimensional analysis of a bioprosthetic heart valve. J Biomech 24:793–801. doi:10.1016/0021-9290(91)90304-6
Bols J, Degroote J, Trachet B, Verhegghe B, Segers P, Vierendeels J (2013) A computational method to assess the in vivo stresses and unloaded configuration of patient-specific blood vessels. J Comput Appl Math 246:10–17. doi:10.1016/j.cam.2012.10.034
Bonomi D et al (2015) Influence of the aortic valve leaflets on the fluid-dynamics in aorta in presence of a normally functioning bicuspid valve. Biomech Model Mechanobiol 14(6):1349–61. doi:10.1007/s10237-015-0679-8
Borghi A, Wood NB, Mohiaddin RH, Xu XY (2008) Fluid-solid interaction simulation of flow and stress pattern in thoracoabdominal aneurysms: a patient-specific study. J Fluid Struct 24:270–280. doi:10.1016/j.jfluidstructs.2007.08.005
Caro CG (1978) The mechanics of the circulation. Oxford University Press, Oxford, New York
Cataloglu A, Gould PL, Clark RE (1975) Validation of a simplified mathematical model for the stress analysis of human aortic heart valves. J Biomech 8:347–348. doi:10.1016/0021-9290(75)90088-3
Causin P, Gerbeau J-F, Nobile F (2005) Added-mass effect in the design of partitioned algorithms for fluid-structure problems. Comput Method Appl Mech Eng 194:4506–4527
Cavalcante JL, Lima JAC, Redheuil A, Al-Mallah MH (2011) Aortic stiffness current understanding and future directions. J Am Coll Cardiol 57:1511–1522. doi:10.1016/j.jacc.2010.12.017
Chew GG, Howard IC, Patterson EA (1999) Simulation of damage in a porcine prosthetic heart valve. J Med Eng Technol 23:178–189
Choo SJ et al (1999) Aortic root geometry: pattern of differences between leaflets and sinuses of Valsalva. J Heart Valve Dis 8:407–415
Clark C (1976) The fluid mechanics of aortic stenosis - II. Unsteady flow experiments. J Biomech 9:567–573
Cochran RP, Kunzelman KS, Chuong CJ, Sacks MS, Eberhart RC (1991) Nondestructive analysis of mitral valve collagen fiber orientation. ASAIO Trans 37:M447–448
Coogan JS, Humphrey JD, Figueroa CA (2013) Computational simulations of hemodynamic changes within thoracic, coronary, and cerebral arteries following early wall remodeling in response to distal aortic coarctation. Biomech Model Mechanobiol 12:79–93. doi:10.1007/s10237-012-0383-x
De Hart J, Baaijens FP, Peters GW, Schreurs PJ (2003) A computational fluid-structure interaction analysis of a fiber-reinforced stentless aortic valve. J Biomech 36:699–712
Del Pin F, Çaldichoury I (2012) LS-DYNA® 980: recent developments, application areas and validation process of the incompressible fluid solver (ICFD) in LS-DYNA Part
Dettmer W, Perić D (2006) A computational framework for fluid-structure interaction: finite element formulation and applications. Comput Method Appl Mech Eng 195:5754–5779. doi:10.1016/j.cma.2005.10.019
Donea J, Giuliani S, Halleux JP (1982) An arbitrary Lagrangian-Eulerian finite element method for transient dynamic fluid-structure interactions. Comput Method Appl Mech Eng 33:689–723. doi:10.1016/0045-7825(82)90128-1
Driessen NJ, Bouten CV, Baaijens FP (2005) Improved prediction of the collagen fiber architecture in the aortic heart valve. J Biomech Eng 127:329–336
Felippa CA, Park K, Farhat C (2001) Partitioned analysis of coupled mechanical systems. Comput Method Appl Mech Eng 190:3247–3270
Förster C, Wall WA, Ramm E (2007) Artificial added mass instabilities in sequential staggered coupling of nonlinear structures and incompressible viscous flows. Comput Method Appl Mech Eng 196:1278–1293
Frauenfelder T et al (2007) In-vivo flow simulation in coronary arteries based on computed tomography datasets: feasibility and initial results. Eur Radiol 17:1291–1300. doi:10.1007/s00330-006-0465-1
Fung Y (1998) Biomechanics: circulation, 2nd edn. Springer, New York
Fung YC (1993) Biomechanics : mechanical properties of living tissues. Springer, New York
Gallo D, Steinman DA, Bijari PB, Morbiducci U (2012) Helical flow in carotid bifurcation as surrogate marker of exposure to disturbed shear. J Biomech 45:2398–2404. doi:10.1016/j.jbiomech.2012.07.007
Garcia D, Camici PG, Durand LG, Rajappan K, Gaillard E, Rimoldi OE, Pibarot P (2009) Impairment of coronary flow reserve in aortic stenosis. J Appl Physiol 106:113–121. doi:10.1152/japplphysiol.00049.2008
Gee MW, Reeps C, Eckstein HH, Wall WA (2009) Prestressing in finite deformation abdominal aortic aneurysm simulation. J Biomech 42:1732–1739. doi:10.1016/j.jbiomech.2009.04.016
Go AS et al (2014) Heart disease and stroke statistics-2014 update: a report from the American Heart Association. Circulation 129:e28–e292. doi:10.1161/01.cir.0000441139.02102.80
Govindjee S, Mihalic PA (1998) Computational methods for inverse deformations in quasi-incompressible finite elasticity. Int J Numer Method Eng 43:821–838
Ha H, Kim GB, Kweon J, Lee SJ, Kim Y-H, Kim N, Yang DH (2016) The influence of the aortic valve angle on the hemodynamic features of the thoracic aorta. Sci Rep 6:32316. doi:10.1038/srep32316
Hallquist JO (2006) LS-DYNA Theory Manual. Livermore Software Technology Corporation
Hamid MS, Sabbah HN, Stein PD (1985) Finite element evaluation of stresses on closed leaflets of bioprosthetic heart valves with flexible stents. Finite Elem Anal Des 1:213–225. doi:10.1016/0168-874X(85)90015-0
Handke M, Heinrichs G, Beyersdorf F, Olschewski M, Bode C, Geibel A (2003) In vivo analysis of aortic valve dynamics by transesophageal 3-dimensional echocardiography with high temporal resolution. J Thorac Cardiovasc Surg 125:1412–1419
He X, Ku DN (1996) Pulsatile flow in the human left coronary artery bifurcation: average conditions. J Biomech Eng 118:74–82
Holzapfel GA, Gasser TC, Ogden RW (2000) A new constitutive framework for arterial wall mechanics and a comparative study of material models. J Elast Phys Sci Solid 61:1–48. doi:10.1023/a:1010835316564
Holzapfel GA, Gasser TC, Ogden RW (2004) Comparison of a multi-layer structural model for arterial walls with a fung-type model, and issues of material stability. J Biomech Eng 126:264–275
Holzapfel GA, Ogden RW (2009) Constitutive modelling of passive myocardium: a structurally based framework for material characterization. Philos Trans R Soc A Math Phys Eng Sci 367:3445–3475. doi:10.1098/rsta.2009.0091
Hope MD, Hope TA, Meadows AK, Ordovas KG, Urbania TH, Alley MT, Higgins CB (2010) Bicuspid aortic valve: four-dimensional MR evaluation of ascending aortic systolic flow patterns. Radiology 255:53–61. doi:10.1148/radiol.09091437
Hsu M-C, Bazilevs Y (2011) Blood vessel tissue prestress modeling for vascular fluid-structure interaction simulation. Finite Elem Anal Des 47:593–599. doi:10.1016/j.finel.2010.12.015
http://www.nature.com/articles/srep32316#supplementary-information
Humphrey JD, Holzapfel GA (2012) Mechanics, mechanobiology, and modeling of human abdominal aorta and aneurysms. J Biomech 45:805–814. doi:10.1016/j.jbiomech.2011.11.021
Humphrey JD, Strumpf RK, Yin FC (1990) Determination of a constitutive relation for passive myocardium: I. A new functional form. J Biomech Eng 112:333–339
Idelsohn SR, Del Pin F, Rossi R, Oñate E (2009) Fluid-structure interaction problems with strong added-mass effect. Int J Numer Method Eng 80:1261–1294. doi:10.1002/nme.2659
Juang D, Braverman AC, Eagle K (2008) Cardiology patient pages. Aortic dissection. Circulation 118:e507–510. doi:10.1161/circulationaha.108.799908
Kamensky D et al (2015) An immersogeometric variational framework for fluid-structure interaction: application to bioprosthetic heart valves. Comput Method Appl Mech Eng 284:1005–1053. doi:10.1016/j.cma.2014.10.040
Katayama S, Umetani N, Sugiura S, Hisada T (2008) The sinus of Valsalva relieves abnormal stress on aortic valve leaflets by facilitating smooth closure J Thorac Cardiovasc Surg 136:1528–1535, 1535.e1521. doi:10.1016/j.jtcvs.2008.05.054
Khanafer K, Berguer R (2009) Fluid-structure interaction analysis of turbulent pulsatile flow within a layered aortic wall as related to aortic dissection. J Biomech 42:2642–2648. doi:10.1016/j.jbiomech.2009.08.010
Ku DN, Giddens DP, Zarins CK, Glagov S (1985) Pulsatile flow and atherosclerosis in the human carotid bifurcation. Positive correlation between plaque location and low oscillating shear stress. Arteriosclerosis 5:293–302
Kunzelman KS, Einstein DR, Cochran RP (2007) Fluid-structure interaction models of the mitral valve: function in normal and pathological states. Philos Trans R Soc Lond B Biol Sci 362:1393–1406. doi:10.1098/rstb.2007.2123
Kunzelman KS, Grande KJ, David TE, Cochran RP, Verrier ED (1994) Aortic root and valve relationships. Impact on surgical repair. J Thorac Cardiovasc Surg 107:162–170
Kunzelman KS, Reimink MS, Cochran RP (1998) Flexible versus rigid ring annuloplasty for mitral valve annular dilatation: a finite element model. J Heart Valve Dis 7:108–116
Labrosse MR, Beller CJ, Robicsek F, Thubrikar MJ (2006) Geometric modeling of functional trileaflet aortic valves: development and clinical applications. J Biomech 39:2665–2672. doi:10.1016/j.jbiomech.2005.08.012
Labrosse MR, Lobo K, Beller CJ (2010) Structural analysis of the natural aortic valve in dynamics: from unpressurized to physiologically loaded. J Biomech 43:1916–1922. doi:10.1016/j.jbiomech.2010.03.020
Lancellotti RM (2012) Numerical computations of deflated vascular geometries for fluid-structure interaction in haemodynamics. Universita degli Studi di Napoli
Lewin MB, Otto CM (2005) The bicuspid aortic valve: adverse outcomes from infancy to old age. Circulation 111:832–834. doi:10.1161/01.cir.0000157137.59691.0b
Leyh RG, Schmidtke C, Sievers HH, Yacoub MH (1999) Opening and closing characteristics of the aortic valve after different types of valve-preserving surgery. Circulation 100:2153–2160
Liu X, Sun A, Fan Y, Deng X (2015) Physiological significance of helical flow in the arterial system and its potential clinical applications. Ann Biomed Eng 43:3–15
Louis Thériault CS, Browarski S (2010) The Canadian heart health strategy: risk factors and future cost implications paper presented at the the conference board of Canada, Ottawa
ICFD Theory Manual. Incompressible fluid solver in LS-DYNA (2013)Livermore Software Technology Corporation (LSTC)
LS-DYNA \(\textregistered \) Keyword User’s Manual, Volume II Material Models (revision: 5442) (2014) Livermore Software Technology Corporation (LSTC)
Martin C, Pham T, Sun W (2011) Significant differences in the material properties between aged human and porcine aortic tissues. Eur J Cardiothorac Surg 40:28–34. doi:10.1016/j.ejcts.2010.08.056
Martufi G, Di Martino ES, Amon CH, Muluk SC, Finol EA (2009) Three-dimensional geometrical characterization of abdominal aortic aneurysms: image-based wall thickness distribution. J Biomech Eng 131:061015. doi:10.1115/1.3127256
May-Newman K, Yin FC (1998) A constitutive law for mitral valve tissue. J Biomech Eng 120:38–47
Mohammadi H (2015) Developing a global fluid-structure interaction model of the aortic root. McGill University, Montreal
Mohammadi H, Cartier R, Mongrain R Development of a 1D model for assessing the aortic root pressure drop with viscosity and compliance. In: ASME 2013 Summer Bioengineering Conference, 2013. American Society of Mechanical Engineers, pp V01AT04A026–V001AT004A026
Mohammadi H, Cartier R, Mongrain R (2015) Derivation of a simplified relation for assessing aortic root pressure drop incorporating wall compliance. Med Biol Eng Comput 53:241–251. doi:10.1007/s11517-014-1228-9
Mohammadi H, Cartier R, Mongrain R (2016a) 3D physiological model of the aortic valve incorporating small coronary arteries. Int J Numer Method Biomed Eng 33(5):e02829. doi:10.1002/cnm.2829
Mohammadi H, Cartier R, Mongrain R (2016) Review of numerical methods for simulation of the aortic root: present and future directions. Int J Comput Method Eng Sci Mech 17:182–195. doi:10.1080/15502287.2016.1189463
Mohammadi H, Cartier R, Mongrain R (2017) The impact of the aortic valve impairment on the distant coronary arteries hemodynamics: a fluid-structure interaction study. Med Biol Eng Comput. doi:10.1007/s11517-017-1636-8
Morbiducci U, Ponzini R, Grigioni M, Redaelli A (2007) Helical flow as fluid dynamic signature for atherogenesis risk in aortocoronary bypass. A numeric study. J Biomech 40:519–534. doi:10.1016/j.jbiomech.2006.02.017
Morbiducci U et al (2008) In vivo quantification of helical blood flow in human aorta by time-resolved three-dimensional cine phase contrast magnetic resonance imaging. Ann Biomed Eng 37:516. doi:10.1007/s10439-008-9609-6
Morganti S, Auricchio F, Benson DJ, Gambarin FI, Hartmann S, Hughes TJR, Reali A (2015) Patient-specific isogeometric structural analysis of aortic valve closure. Comput Method Appl Mech Eng 284:508–520. doi:10.1016/j.cma.2014.10.010
Mozaffarian D et al (2016) Executive summary: heart disease and stroke statistics-2016 update: a report from the American Heart Association. Circulation 133:447
Nemes A, Forster T, Lengyel C, Csanady M (2007) Reduced aortic distensibility and coronary flow velocity reserve in diabetes mellitus patients with a negative coronary angiogram. Can J Cardiol 23:445–450
Nestola MG et al (2017) Computational comparison of aortic root stresses in presence of stentless and stented aortic valve bio-prostheses. Comput Method Biomech Biomed Eng 20:171–181. doi:10.1080/10255842.2016.1207171
Nishimura RA et al (2014) 2014 AHA/ACC guideline for the management of patients with valvular heart disease a report of the American College of Cardiology/American Heart Association task force on practice guidelines. J Am Coll Cardiol. doi:10.1016/j.jacc.2014.02.536
Nobari S, Mongrain R, Gaillard E, Leask R, Cartier R (2012) Therapeutic vascular compliance change may cause significant variation in coronary perfusion: a numerical study. Comput Math Method Med 2012:791686. doi:10.1155/2012/791686
Nobari S, Mongrain R, Leask R, Cartier R (2013) The effect of aortic wall and aortic leaflet stiffening on coronary hemodynamic: a fluid-structure interaction study. Med Biol Eng Comput 51:923–936. doi:10.1007/s11517-013-1066-1
Nosovitsky VA, Ilegbusi OJ, Jiang J, Stone PH, Feldman CL (1997) Effects of curvature and stenosis-like narrowing on wall shear stress in a coronary artery model with phasic flow. Comput Biomed Res 30:61–82
Oberoi S, Schoepf UJ, Meyer M, Henzler T, Rowe GW, Costello P, Nance JW (2013) Progression of arterial stiffness and coronary atherosclerosis: longitudinal evaluation by cardiac CT. Am J Roentgenol 200:798–804. doi:10.2214/AJR.12.8653
Patterson EA, Howard IC, Thornton MA (1996) A comparative study of linear and nonlinear simulations of the leaflets in a bioprosthetic heart valve during the cardiac cycle. J Med Eng Technol 20:95–108
Perktold K, Resch M, Peter RO (1991) Three-dimensional numerical analysis of pulsatile flow and wall shear stress in the carotid artery bifurcation. J Biomech 24:409–420
Politis AK, Stavropoulos GP, Christolis MN, Panagopoulos FG, Vlachos NS, Markatos NC (2007) Numerical modeling of simulated blood flow in idealized composite arterial coronary grafts: steady state simulations. J Biomech 40:1125–1136. doi:10.1016/j.jbiomech.2006.05.008
Prot V, Skallerud B, Holzapfel GA (2007) Transversely isotropic membrane shells with application to mitral valve mechanics. Constitutive modelling and finite element implementation. Int J Numer Method Eng 71:987–1008. doi:10.1002/nme.1983
Qiu Y, Tarbell JM (2000) Numerical simulation of pulsatile flow in a compliant curved tube model of a coronary artery. J Biomech Eng 122:77–85
Quapp KM, Weiss JA (1998) Material characterization of human medial collateral ligament. J Biomech Eng 120:757–763
Ranga A, Bouchot O, Mongrain R, Ugolini P, Cartier R (2006) Computational simulations of the aortic valve validated by imaging data: evaluation of valve-sparing techniques. Interact Cardiovasc Thorac Surg 5:373–378. doi:10.1510/icvts.2005.121483
Rossow MP, Gould PL, Clark RE (1978) A simple method for estimating stresses in natural and prosthetic heart valves. Biomater Med Devices Artif Organs 6:277–290
Sabbah HN, Hamid MS, Stein PD (1986) Mechanical stresses on closed cusps of porcine bioprosthetic valves: correlation with sites of calcification. Ann Thorac Surg 42:93–96
Sacks MS (2003) Incorporation of experimentally-derived fiber orientation into a structural constitutive model for planar collagenous tissues. J Biomech Eng 125:280–287
Sahasakul Y, Edwards WD, Naessens JM, Tajik AJ (1988) Age-related changes in aortic and mitral valve thickness: implications for two-dimensional echocardiography based on an autopsy study of 200 normal human hearts. Am J Cardiol 62:424–430
Shanmugavelayudam SK, Rubenstein DA, Yin W (2010) Effect of geometrical assumptions on numerical modeling of coronary blood flow under normal and disease conditions. J Biomech Eng 132:061004. doi:10.1115/1.4001033
Smith S, Austin S, Wesson GD, Moore CA (2006) Calculation of wall shear stress in left coronary artery bifurcation for pulsatile flow using two-dimensional computational fluid dynamics. Conf Proc IEEE Eng Med Biol Soc 1:871–874. doi:10.1109/iembs.2006.260101
Sun W, Abad A, Sacks MS (2005) Simulated bioprosthetic heart valve deformation under quasi-static loading. J Biomech Eng 127:905–914
Tadros TM, Klein MD, Shapira OM (2009) Ascending aortic dilatation associated with bicuspid aortic valve: pathophysiology, molecular biology, and clinical implications. Circulation 119:880–890. doi:10.1161/circulationaha.108.795401
Taylor CA, Hughes TJ, Zarins CK (1998) Finite element modeling of three-dimensional pulsatile flow in the abdominal aorta: relevance to atherosclerosis. Ann Biomed Eng 26:975–987
Thubrikar M (1990) The aortic valve. CRC Press, Boca Raton
Thubrikar MJ, Heckman JL, Nolan SP (1993) High speed cine-radiographic study of aortic valve leaflet motion. J Heart Valve Dis 2:653–661
Tremblay D, Zigras T, Cartier R, Leduc L, Butany J, Mongrain R, Leask RL (2009) A comparison of mechanical properties of materials used in aortic arch reconstruction. Ann Thorac Surg 88:1484–1491. doi:10.1016/j.athoracsur.2009.07.023
Tse KM, Chiu P, Lee HP, Ho P (2011) Investigation of hemodynamics in the development of dissecting aneurysm within patient-specific dissecting aneurismal aortas using computational fluid dynamics (CFD) simulations. J Biomech 44:827–836. doi:10.1016/j.jbiomech.2010.12.014
van Loon R (2010) Towards computational modelling of aortic stenosis. Int J Numer Method Biomed Eng 26:405–420. doi:10.1002/cnm.1270
van Loon R, Anderson PD, de Hart J, Baaijens FPT (2004) A combined fictitious domain/adaptive meshing method for fluid-structure interaction in heart valves. Int J Numer Method Fluids 46:533–544. doi:10.1002/fld.775
Weinberg EJ, Kaazempur-Mofrad MR (2005) On the constitutive models for heart valve leaflet mechanics. Cardiovasc Eng 5:37–43. doi:10.1007/s10558-005-3072-x
Weinberg EJ, Kaazempur-Mofrad MR (2006) A large-strain finite element formulation for biological tissues with application to mitral valve leaflet tissue mechanics. J Biomech 39:1557–1561. doi:10.1016/j.jbiomech.2005.04.020
Weinberg EJ, Shahmirzadi D, Mofrad MR (2010) On the multiscale modeling of heart valve biomechanics in health and disease. Biomech Model Mechanobiol 9:373–387. doi:10.1007/s10237-009-0181-2
Yearwood TL, Misbach GA, Chandran KB (1989) Experimental fluid dynamics of aortic stenosis in a model of the human aorta. Clin Phys Physiol Meas 10:11–24
Zamir M (2005) The physics of coronary blood flow. Springer. http://worldcat.org http://public.eblib.com/EBLPublic/PublicView.do?ptiID=302787
Zygote Media Group I (2011) The Zygote Solid 3D Heart Model
Acknowledgements
This research was supported by McGill Engineering Doctoral Award (MEDA), NSERC and Montreal Heart institute (MHI). This work was made possible by the facilities of the Shared Hierarchical Academic Research Computing Network (SHARCNET: www.sharcnet.ca) and Compute/Calcul Canada.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Rights and permissions
About this article
Cite this article
Mohammadi, H., Cartier, R. & Mongrain, R. Fiber-reinforced computational model of the aortic root incorporating thoracic aorta and coronary structures. Biomech Model Mechanobiol 17, 263–283 (2018). https://doi.org/10.1007/s10237-017-0959-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10237-017-0959-6