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Mechanical Models of Artery Walls

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Abstract

The article presents the up to date review and discussion of approaches used to express mechanical behavior of artery walls. The physiology of artery walls and its relation to the models is discussed. Presented models include the simplest 0d and 1d ones but emphasis is put to the most sophisticated approaches which are based on the theory of 3d nonlinear elasticity. Also the alternative approach which consists in simple delinearization of the Koiter shell equations is presented.

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References

  1. Antman SS (1995) Nonlinear problems of elasticity. Springer, New York

    MATH  Google Scholar 

  2. Ball JM (1977) Convexity conditions and existence theorems in nonlinear elasticity. Arch Ration Mech Anal 63(4):337–403

    MATH  Google Scholar 

  3. Balzani D, Neff P, Schröder J, Holzapfel GA (2006) A polyconvex framework for soft biological tissues. Adjustment to experimental data. Int J Solids Struct 43(20):6052–6070

    MATH  Google Scholar 

  4. Bazilevs Y, Calo VM, Zhang Y, Hughes TJR (2006) Isogeometric fluid-structure interaction analysis with applications to arterial blood flow. Comput Mech 38(4–5):310–322

    MathSciNet  MATH  Google Scholar 

  5. Bergel DH (1961) The static elastic properties of the arterial wall. J Physiol 156(3):445–457

    Google Scholar 

  6. Biazutti AC (1995) On a nonlinear evolution equation and its applications. Nonlinear Anal Theory Methods Appl 24(8):1221–1234

    MATH  MathSciNet  Google Scholar 

  7. Bischoff JE (2006) Reduced parameter formulation for incorporating fiber level viscoelasticity into tissue level biomechanical models. Ann Biomed Eng 34(7):1164–1172

    MathSciNet  Google Scholar 

  8. Bischoff JE, Arruda EA, Grosh K (2002) Finite element simulations of orthotropic hyperelasticity. Finite Elem Anal Des 38(10):983–998

    MATH  Google Scholar 

  9. Bischoff JE, Arruda EA, Grosh K (2002) A microstructurally based orthotropic hyperelastic constitutive law. J Appl Mech 69(5):570–579

    MATH  Google Scholar 

  10. Bischoff JE, Arruda EA, Grosh K (2004) A rheological network model for the continuum anisotropic and viscoelastic behavior of soft tissue. Biomech Model Mechanobiol 3(1):56–65

    Google Scholar 

  11. Brossollet LJ, Vito RP (1996) A new approach to mechanical testing and modeling of biological tissues, with application to blood vessels. J Biomech Eng 118(4):433–439

    Google Scholar 

  12. Brown RE, Butler JP, Rogers RA, Leith DE (1994) Mechanical connections between elastin and collagen. Connect Tissue Res 30(4):295–308

    Google Scholar 

  13. Burton AC (1954) Relation of structure to function of the tissues of the wall of blood vessels. Physiol Rev 34:619–642

    Google Scholar 

  14. Canic S, Mikelic A (2003) Effective equations modeling the flow of a viscous incompressible fluid through a long elastic tube arising in the study of blood flow through small arteries. SIAM J Appl Dyn Syst 2(3):431–463

    MATH  MathSciNet  Google Scholar 

  15. Canic S, Lamponi D, Mikelic A, Tambaca J (2005) Self-consistent effective equations modeling blood flow in medium-to-large compliant arteries. Multiscale Model Simul 3(3):559–596

    MATH  MathSciNet  Google Scholar 

  16. Canic S, Mikelic A, Tambaca J (2005) A two-dimensional effective model describing fluid-structure interaction in blood flow: analysis, simulation and experimental validation. C R Mech Acad Sci Paris 333(12):867–883

    Google Scholar 

  17. Canic S, Hartley CJ, Rosenstrauch D, Tambaca J, Guidoboni G, Mikelic A (2006) Blood flow in compliant arteries: an effective viscoelastic reduced model, numerics and experimental validation. Ann Biomed Eng 34(4):572–592

    Google Scholar 

  18. Canic S, Tambaca J, Guidoboni G, Mikelic A, Hartley CJ, Rosenstrauch D, Humphrey JD (2006) Modeling viscoelastic behavior of arterial walls and their interaction with pulsatile blood flow. SIAM J Appl Math 67(1):164–193

    MATH  MathSciNet  Google Scholar 

  19. Causin P, Gerbeau JF, Nobile F (2005) Added-mass effect in the design of partitioned algorithms for fluid-structure problems. Comput Methods Appl Mech Eng 194(42–44):4506–4527

    MATH  MathSciNet  Google Scholar 

  20. Chakravarty S, Mandal PK, Mandal A (2004) Numerical simulation of unsteady two-layered pulsatile blood flow in a stenosed flexible artery: effect of peripheral layer viscosity. Math Model Anal 9(2):99–114

    MATH  MathSciNet  Google Scholar 

  21. Chuong CJ, Fung YC (1983) Three-dimensional stress distribution in arteries. J Biomech Eng 105(3):268–274

    Google Scholar 

  22. Chuong CJ, Fung YC (1984) Compressibility and constitutive equation of arterial wall in radial compression experiments. J Biomech 17(1):35–40

    Google Scholar 

  23. Ciarlet PG (1988) Mathematical elasticity. Volume I: three-dimensional elasticity. Elsevier, Amsterdam

    MATH  Google Scholar 

  24. Ciarlet PG (2000) Mathematical elasticity. Vol. III, theory of shells. Elsevier, Amsterdam

    MATH  Google Scholar 

  25. Clark JM, Glagov S (1985) Transmural organization of the arterial media. The lamellar unit revisited. Arterioscler Thromb Vasc Biol 5:19–34

    Google Scholar 

  26. Cole RT, Lucas CL, Cascio WE, Johnson TA (2005) A labviewTM model incorporating an open-loop arterial impedance and a closed-loop circulatory system. Ann Biomed Eng 33(11):1555–1573

    Google Scholar 

  27. Comninou M, Yannas IV (1976) Dependence of stress-strain nonlinearity of connective tissues on the geometry of collagen fibers. J Biomech 9(7):427–433

    Google Scholar 

  28. Conlon MJ, Rusell DL, Mussivand T (2006) Development of a mathematical model of the human circulatory system. Ann Biomed Eng 34(9):1400–1413

    Google Scholar 

  29. Davies PF, Spaan JA, Krams R (2005) Shear stress biology of the endothelium. Ann Biomed Eng 33(12):1714–1718

    Google Scholar 

  30. Delfino A, Stergiopulos N, Moore JE, Meister J-J (1997) Residual strain effects on the stress field in a thick wall finite element model of the human carotid bifurcation. J Biomech 30(8):777–786

    Google Scholar 

  31. Demiray H, Vito RP (1983) On large periodic motions of arteries. J Biomech 16(8):643–648

    Google Scholar 

  32. Demiray H, Vito RP (1991) A layered cylindrical shell model for an aorta. Int J Eng Sci 29(1):47–54

    MATH  Google Scholar 

  33. Dixon SA, Heikes RG, Vito RP (2003) Constitutive modeling of porcine coronary arteries using designed experiments. J Biomech Eng 125(2):274–279

    Google Scholar 

  34. Dobrin PB (1999) Distribution of lamellar deformations: implications for properties of the arterial media. Hypertension 33(3):806–810

    Google Scholar 

  35. Doyle JM, Dobrin PB (1971) Finite deformation analysis of the relaxed and contracted dog carotid artery. Microvasc Res 3(4):400–415

    Google Scholar 

  36. Driessen NJB, Wilson W, Bouten CVC, Baaijens FPT (2004) A computational model for collagen fibre remodelling in the arterial wall. J Theor Biol 226(1):53–64

    Google Scholar 

  37. Dyson F (2004) Turning points. A meeting with Enrico Fermi. Nature 427:297

    Google Scholar 

  38. Evans LC (1998) Partial differential equations. American Mathematical Society, Providence

    MATH  Google Scholar 

  39. Fernández ÁM, Milisic V, Quarteroni A (2005) Analysis of a geometrical multiscale blood flow model based on the coupling of ODEs and hyperbolic PDEs. Multisc Model Simul 4(1):215–236

    MATH  Google Scholar 

  40. Figueroa CA, Vignon-Clementel IE, Jansen KE, Hughes TJR, Taylor CA (2006) A coupled momentum method for modeling blood flow in three-dimensional deformable arteries. Comput Methods Appl Mech Eng 195(41–43):5685–5706

    MATH  MathSciNet  Google Scholar 

  41. Formaggia L, Veneziani A (2003) Reduced and multiscale models for the human cardiovascular system. Reports of Laboratory for Modeling and Scientific Computing MOX, Politecnica di Milano, 21

  42. Formaggia L, Nobile F, Quarteroni A, Veneziani A (1999) Multiscale modelling of the circulatory system: a preliminary analysis. Comput Vis Sci 2(2–3):75–83

    MATH  Google Scholar 

  43. Fung YC (1967) Elasticity of soft tissues in simple elongation. Am J Physiol Leg Content 231(6):1532–1544

    Google Scholar 

  44. Fung YC (1993) Biomechanics: mechanical properties of living tissues. Springer, New York

    Google Scholar 

  45. Fung YC, Fronek K, Patitucci P (1979) Pseudoelasticity of arteries and the choice of its mathematical expression. Am J Physiol Heart Circ Physiol 237(5):H620–H631

    Google Scholar 

  46. Fung YC, Liu SQ, Zhou JB (1993) Remodeling of the constitutive equation while a blood vessel remodels itself under stress. J Biomech Eng 115(4B):453–459

    Google Scholar 

  47. Gajewski H, Gröger K, Zacharias K (1974) Nichtlineare operatorgleichungen und operatordifferentialgleichungen. Akademie, Berlin

    MATH  Google Scholar 

  48. Gasser TC, Holzapfel GA (2002) A rate-independent elastoplastic constitutive model for biological fiber-reinforced composites at finite strains: continuum basis, algorithmic formulation and finite element implementation. Comput Mech 29(4–5):340–360

    MATH  Google Scholar 

  49. Gasser TC, Ogden RW, Holzapfel GA (2006) Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J R Soc Interface 3(6):15–35

    Google Scholar 

  50. Glagov S, Vito R, Giddens DP, Zarins CK (1992) Micro-architecture and composition of artery walls: relationship to location, diameter and the distribution of mechanical stress. J Hypertens Suppl 10(6):S101–S104

    Google Scholar 

  51. Gleason RL, Humphrey JD (2005) A 2d constrained mixture model for arterial adaptations to large changes in flow, pressure and axial stretch. Math Med Biol 22(4):347–369

    MATH  Google Scholar 

  52. Gosling RG, Budge MM (2003) Terminology for describing the elastic behavior of arteries. Hypertension 41(6):1180–1182

    Google Scholar 

  53. Greenwald SE (2002) Pulse pressure and arterial elasticity. QJM: Int J Med 95(2):107–112

    Google Scholar 

  54. Hamadiche M, Kizilova N (2005) Temporal and spatial instabilities of the flow in the blood vessels as multi-layered compliant tubes. Int J Dyn Fluids 1(1):1–24

    Google Scholar 

  55. Haslach HW (2005) Nonlinear viscoelastic, thermodynamically consistent, models for biological soft tissue. Biomech Model Mechanobiol 3(3):172–189

    Google Scholar 

  56. Hayashi K (2003) Mechanical properties of soft tissues and arterial walls. In: Holzapfel GA, Ogden RW (eds) Biomechanics of soft tissue in cardiovascular system. Springer, New York, pp 15–64

    Google Scholar 

  57. Hayashi K, Washizu T, Tsushima N, Kiraly RJ, Nose Y (1981) Mechanical properties of aortas and pulmonary arteries of calves implanted with cardiac prostheses. J Biomech 14(3):173–182

    Google Scholar 

  58. Hayashi K, Stergiopulos N, Meister J-J, Greenwald SE, Rachev A (2001) Techniques in the determination of the mechanical properties and constitutive laws of arterial walls. In: Leondes CT (ed) Cardiovascular techniques. Biomechanical systems: techniques and applications, vol 2. CRC Press, Boca Raton

    Google Scholar 

  59. Hokanson J, Yazdani S (1997) A constitutive model of the artery with damage. Mech Res Commun 24(2):151–159

    MATH  Google Scholar 

  60. Holzapfel GA (2000) Nonlinear solid mechanics, a continuum approach for engineering. Wiley, Chichester

    MATH  Google Scholar 

  61. Holzapfel GA (2003) Structural and numerical models for the (visco)elastic response of arterial walls with residual stresses. In: Holzapfel GA, Ogden RW (eds) Biomechanics of soft tissue in cardiovascular system. Springer, New York, pp 109–184

    Google Scholar 

  62. Holzapfel GA, Gasser TC (2001) A viscoelastic model for fiber-reinforced composites at finite stains: continuum basis, computational aspects and applications. Comput Methods Appl Mech Eng 190(34):4379–4403

    Google Scholar 

  63. Holzapfel GA, Gasser TC (2007) Computational stress-deformation analysis of arterial walls including high-pressure response. Int J Cardiol 116(1):78–85

    Google Scholar 

  64. Holzapfel GA, Weizsäcker HW (1998) Biomechanical behavior of the arterial wall and its numerical characterization. Comput Biol Med 28(4):377–392

    Google Scholar 

  65. Holzapfel GA, Ogden RW (eds) (2006) Mechanics of biological tissue. Springer, New York

    Google Scholar 

  66. Holzapfel GA, Gasser TC, Ogden RW (2000) A new constitutive framework for arterial wall mechanics and a comparative study of material models. J Elast 61(1-3):1–48

    MATH  MathSciNet  Google Scholar 

  67. Holzapfel GA, Gasser TC, Stadler M (2002) A structural model for the viscoelastic behavior of arterial walls: continuum formulation and finite element analysis. Eur J Mech A: Solids 21(3):441–463

    Article  MATH  Google Scholar 

  68. 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(2):264–275

    Google Scholar 

  69. Horgan CO, Saccomandi G (2003) A description of arterial wall mechanics using limiting chain extensibility constitutive models. Biomech Model Mechanobiol 1(4):251–266

    Google Scholar 

  70. Hron J (2001) Fluid structure interaction with applications in biomechanics. PhD thesis, Faculty of Mathematics and Physics, Charles University in Prague

  71. Humphrey JD (1995) Mechanics of the arterial wall: review and directions. Crit Rev Biomed Eng 23(1-2):1–162

    Google Scholar 

  72. Humphrey JD (2002) Cardiovascular solid mechanics: cells, tissues, and organs. Springer, New York

    Google Scholar 

  73. Humphrey JD (2003) Continuum biomechanics of soft biological tissues. Proc R Soc A: Math Phys Eng Sci 459(2029):3–46

    MATH  MathSciNet  Google Scholar 

  74. Humphrey JD (2003) Intracranial saccular aneurysms. In: Holzapfel GA, Ogden RW (eds) Biomechanics of soft tissue in cardiovascular system. Springer, New York, pp 185–220

    Google Scholar 

  75. Humphrey JD, Canham PB (2000) Structure, mechanical properties, and mechanics of intracranial saccular aneurysms. J Elast 61(1–3):49–81

    MATH  Google Scholar 

  76. Humphrey JD, Na S (2002) Elastodynamics and arterial wall stress. Ann Biomed Eng 30(4):509–523

    Google Scholar 

  77. Itskov M, Ehret AE, Mavrilas D (2006) A polyconvex anisotropic strain-energy function for soft collagenous tissues. Biomech Model Mechanobiol 5(1):17–26

    Google Scholar 

  78. John LR (2004) Forward electrical transmission line model of the human arterial system. Med Biol Eng Comput 42(3):312–321

    Google Scholar 

  79. Kalita P (2005) Algorithms for solving nonlinear problems in artery dymamics. PhD thesis, Jagiellonian University, Cracow

  80. Kalita P, Schaefer R (2005) Dynamics of the weakly nonlinear Koiter shell. In: Pietraszkiewicz W, Szymczak C (eds) Shell structures: theory and applications. Taylor & Francis/Balkema, London, pp 125–128

    Google Scholar 

  81. Kalita P, Schaefer R, Paszyński M (2006) Nonlinear models of artery dynamics. In: Fotiadis DI, Massalas CV (eds) Mathematical methods in scattering theory and biomedical engineering. World Scientific, London, pp 320–334

    Google Scholar 

  82. Kasyanov VA, Rachev AI (1980) Deformation of blood vessels upon stretching, internal pressure, and torsion. Mech Compos Mater 16(1):76–80

    Google Scholar 

  83. Keener J, Sneyd J (1998) Mathematical physiology. Springer, New York

    MATH  Google Scholar 

  84. Kleinstreuer C, Hyun S, Archie JP (2000) Computer-aided design and optimal surgical reconstruction of the carotid artery bifurcation. In: Martonen TB (ed) Medical application of computer modeling: cardiovascular and ocular systems. WIT Press, London

    Google Scholar 

  85. Kreiss HO, Peterson NA, Yström J (2002) Difference approximations for the second order wave equation. SIAM J Numer Anal 40(5):1940–1967

    MATH  MathSciNet  Google Scholar 

  86. Laganá K, Balossino R, Migliavacca F, Pennati G, Bove EL, de Leval MR, Dubini G (2005) Multiscale modeling of the cardiovascular system: application to the study of pulmonary and coronary perfusions in the univentricular circulation. J Biomech 38(5):1129–1141

    Google Scholar 

  87. Langille BL, Bendeck MP, Keeley FW (1989) Adaptations of carotid arteries of young and mature rabbits to reduced carotid blood flow. Am J Physiol Heart Circ Physiol 256(4):H931–H939

    Google Scholar 

  88. Li Z, Kleinstreuer C (2005) A new wall stress equation for aneurysm-rupture prediction. Ann Biomed Eng 33(2):209–213

    Google Scholar 

  89. Lieber BB (2000) Arterial macrocirculatory hemodynamics. In: Bronzino J (ed) The biomedical engineering handbook, vol 1, 2nd edn. CRC Press, Boca Raton

    Google Scholar 

  90. Ling SC, Chow CH (1977) The mechanics of corrugated collagen fibrils in arteries. J Biomech 10(2):71–77

    Google Scholar 

  91. Mase GT, Mase GE (1999) Continuum mechanics for engineers. CRC Press, Boca Raton

    MATH  Google Scholar 

  92. Matsumoto T, Hayashi K (1994) Mechanical and dimensional adaptation of rat aorta to hypertension. J Biomech Eng 116(3):278–283

    Google Scholar 

  93. Mohan D, Melvin JW (1983) Failure properties of passive human aortic tissue. ii—biaxial tension tests. J Biomech Eng 16(1):31–44

    Google Scholar 

  94. Moore JE, Delfino A, Doriot P-A, Dorsaz P-A, Rutishauser W (2001) Arterial fluid dynamics: the relationship to atherosclerosis and application in diagnostics. In: Leondes CT (ed) Biofluid methods in vascular and pulmonary systems. Biomechanical systems techniques and applications, vol 4. CRC Press, Boca Raton

    Google Scholar 

  95. Nerem RM (1992) Vascular fluid mechanics, the arterial wall, and atherosclerosis. J Biomech Eng 114(3):274–282

    Google Scholar 

  96. Ogden RW (2003) Nonlinear elasticity, anisotropy, material stability and residual stresses in soft tissue. In: Holzapfel GA, Ogden RW (eds) Biomechanics of soft tissue in cardiovascular system. Springer, New York, pp 65–108

    Google Scholar 

  97. Ogden RW (2003) Nonlinear elasticity with applications to material modelling. Lecture notes 6. IPPT PAN and CoE AMAS, Warsaw

  98. Olsson T, Stålhand J, Klarbring A (2006) Modeling initial strain distribution in soft tissues with application to arteries. Biomech Model Mechanobiol 5(1):27–38

    Google Scholar 

  99. Olufsen MS (1998) Modeling the arterial system with reference to an anesthesia simulator. PhD thesis, Department of Mathematics, Roskilde University

  100. Olufsen MS, Nadim A (2004) On deriving lumped models for blood flow and pressure in the systemic arteries. Math Biosci Eng 1(1):61–80

    MATH  MathSciNet  Google Scholar 

  101. Ottesen JT, Olufsen MS, Larsen JK (2004) Mathematical models in human physiology. Society for Industrial and Applied Mathematics, Philadelphia

    MATH  Google Scholar 

  102. Paszynski M, Schaefer R (2005) The modified fluid particle model for non-linear Casson fluid and its parallel distributed implementation. Comput Methods Appl Mech Eng 194(42–44):4386–4410

    MATH  Google Scholar 

  103. Perktold K, Leuprecht A, Prosi M, Berk T, Czerny M, Trubel W, Schima H (2002) Fluid dynamics, wall mechanics, and oxygen transfer in peripheral bypass anastomoses. Ann Biomed Eng 30(4):447–460

    Google Scholar 

  104. Pontrelli G, Rossoni E (2003) Numerical modelling of the pressure wave propagation in the arterial flow. Int J Numer Methods Fluids 43(6-7):651–671

    MATH  MathSciNet  Google Scholar 

  105. Quaglini V, Vena P, Contro R (2004) A discrete-time approach to the formulation of constitutive models for viscoelastic soft tissues. Biomech Model Mechanobiol 3(2):85–97

    Google Scholar 

  106. Quarteroni A, Formaggia L (2004) Mathematical modelling and numerical simulation of the cardiovascular system. In: Ayache N (ed) Handbook of numerical analysis, volume XII: special volume: computational models for the human body. Elsevier, Amsterdam

    Google Scholar 

  107. Quarteroni A, Veneziani A (2003) Analysis of a geometrical multiscale model based on the coupling of ODEs and PDEs for blood flow simulations. Multiscale Model Simul 1(2):173–195

    MATH  MathSciNet  Google Scholar 

  108. Quarteroni A, Tuveri M, Veneziani A (2000) Computational vascular fluid dynamics: problems, models and methods. Comput Vis Sci 2:163–197

    MATH  Google Scholar 

  109. Quarteroni A, Ragni S, Veneziani A (2001) Coupling between lumped and distributed models for blood flow problems. Comput Vis Sci 4(2):111–124

    MATH  MathSciNet  Google Scholar 

  110. Rachev A (1997) Theoretical study of the effect of stress-dependent remodeling on arterial geometry under hypertensive conditions. J Biomech 30(8):819–827

    Google Scholar 

  111. Rachev A (2000) A model of arterial adaptation to alterations in blood flow. J Elast 61(1-3):83–111

    MATH  MathSciNet  Google Scholar 

  112. Rachev A (2003) Remodeling of arteries in response to changes in their mechnical environment. In: Holzapfel GA, Ogden RW (eds) Biomechanics of soft tissue in cardiovascular system. Springer, New York, pp 221–272

    Google Scholar 

  113. Rachev A, Hayashi K (1999) Theoretical study of the effects of vascular smooth muscle contraction on strain and stress distributions in arteries. Ann Biomed Eng 27(4):459–468

    Google Scholar 

  114. Richardson PD (2002) Biomechanics of plaque rupture: progress, problems, and new frontiers. Ann Biomed Eng 30(4):524–536

    Google Scholar 

  115. Schaefer R, Sedziwy S (2000) Filtration in cohesive soils: numerical approach. CAMES 6:15–26

    MathSciNet  Google Scholar 

  116. Schneck DJ (2000) An outline of cardiovascular structure and function. In: Bronzino J (ed) The biomedical engineering handbook, vol 1, 2nd edn. CRC Press, Boca Raton

    Google Scholar 

  117. Segers P, Stergiopulos N, Verdonck P, Verhoeven R (1997) Assessment of distributed arterial network models. Med Biol Eng Comput 35(6):729–736

    Google Scholar 

  118. Shadwick RE (1999) Mechanical design in arteries. J Exp Biol 202(23):3305–3313

    Google Scholar 

  119. Shah AD, Humphrey JD (1999) Finite strain elastodynamics of intracranial saccular aneurysms. J Biomech 32(6):593–599

    Google Scholar 

  120. Silver FH, Horvath I, Foran DJ (2001) Viscoelasticity of the vessel wall: the role of collagen and elastic fibers. Crit Rev Biomed Eng 29(3):279–301

    Google Scholar 

  121. Simo JC, Taylor RL, Pister KS (1985) Variational and projection methods for the volume constraint in finite deformation elasto-plasticity. Comput Methods Appl Mech Eng 51(1–3):177–208

    MATH  MathSciNet  Google Scholar 

  122. Simon BR, Kaufmann MV, McAfee MA, Baldwin AL, Wilson LM (1998) Identification and determination of material properties for porohyperelastic analysis of large arteries. J Biomech Eng 120(2):188–194

    Google Scholar 

  123. Solomon EP, Schmidt R, Ardragna P (1990) Human anatomy and physiology. Saunders College Publishing, Philadelphia

    Google Scholar 

  124. Stålhand J, Klarbring A (2005) Aorta in vivo parameter identification using an axial force constraint. Biomech Model Mechanobiol 3(4):191–199

    Google Scholar 

  125. Stålhand J, Klarbring A, Karlsson M (2004) Towards in vivo aorta material identification and stress estimation. Biomech Model Mechanobiol 2(3):169–186

    Google Scholar 

  126. Stergiopulos N, Meister J-J (1996) Biomechanical and physiological aspects of arterial vasomotion. In: Jaffrin MY, Caro C (eds) Biological flows. Plenum, New York, pp 137–158

    Google Scholar 

  127. Stergiopulos N, Westerhof BE, Westerhof N (1999) Total arterial inertance as the fourth element of the Windkessel model. Am J Physiol Heart Circ Physiol 276(1):H81–H88

    Google Scholar 

  128. Taber LA (1998) A model for aortic growth based on fluid shear and fiber stresses. J Biomech Eng 120(3):348–354

    Google Scholar 

  129. Takamizawa K, Hayashi K (1987) Strain energy density function and uniform strain hypothesis for arterial mechanics. J Biomech 20(1):7–17

    Google Scholar 

  130. Tanaka TT, Fung YC (1974) Elastic and inelastic properties of the canine aorta and their variation along the aortic tree. J Biomech 7(4):357–370

    Google Scholar 

  131. Timmons WD (2000) Cardiovascular models and control. In: Bronzino J (ed) The biomedical engineering handbook, vol 2, 2nd edn. CRC Press, Boca Raton

    Google Scholar 

  132. Tucker WK, Janicki JS, Plowman F, Patel DJ (1969) A device to test mechanical properties of tissues and transducers. J Appl Physiol 26(5):656–658

    Google Scholar 

  133. Ursino M, Cristalli C (2001) Techniques and applications of mathematical modeling for noninvasive blood pressure estimation. In: Leondes CT (ed) Cardiovascular techniques. Biomechanical systems: techniques and applications, vol 2. CRC Press, Boca Raton

    Google Scholar 

  134. Usyk TP, McCulloch AD (2003) Computational methods for soft tissue biomechanics. In: Holzapfel GA, Ogden RW (eds) Biomechanics of soft tissue in cardiovascular system. Springer, New York, pp 273–342

    Google Scholar 

  135. Vaishnav RN, Vassoughi J (1983) Estimation of residual stresses in aortic segments. In: Hall CW (ed) Biomedical engineering II, recent developments. Pergamon, New York, pp 330–333

    Google Scholar 

  136. Vaishnav RN, Young JT, Patel DJ (1973) Distribution of stresses and of strain-energy density through the wall thickness in a canine aortic segment. Circ Res 32(5):577–583

    Google Scholar 

  137. Valenta J, Vitek K, Cihak R, Konvickova S, Sochor M, Horny L (2002) Age related constitutive laws and stress distribution in human main coronary arteries with reference to residual strain. Bio-Med Mater Eng 12(2):121–134

    Google Scholar 

  138. van Dam EA, Dams SD, Peters GWM, Rutten MCM, Schurink GWH, Buth J, van de Vosse FN (2006) Determination of linear viscoelastic behavior of abdominal aortic aneurysm thrombus. Biorheology 43(6):695–707

    Google Scholar 

  139. van de Vosse FN (2005) Wave propagation in arteries, coronary circulation or aneurysms. In: Kowalewski TA, van Steenhoven A, Nowicki A (eds) Materials of blood flow—modelling and diagnostics advanced course and workshop—BF 2005. Institute of Fundamental Technological Research, Warsaw

    Google Scholar 

  140. van de Vosse FN, de Hart J, van Oijen CHGA, Bessems D, Gunther TWM, Segal A, Wolters BJBM, Stijnen JMA, Baaijens FPT (2003) Finite-element-based computational methods for cardiovascular fluid-structure interaction. J Eng Math 47(3-4):335–368

    MATH  Google Scholar 

  141. Veress AI, Vince DG, Anderson PM, Cornhill JF, Herderick EE, Klingensmith JD, Kuban BD, Greenberg NL, Thomas JD (2000) Vascular mechanics of the coronary artery. Z Kardiol 89(14):S092–S100

    Google Scholar 

  142. Vito RP, Dixon SA (2003) Blood vessel constitutive models—1995–2002. Annu Rev Biomed Eng 5(4–5):413–439

    Google Scholar 

  143. von Maltzahn WW, Warriyar RG, Keitzer WF (1984) Experimental measurements of elastic properties of media and adventitia of bovine carotid arteries. J Biomech 17(11):839–847

    Google Scholar 

  144. Vorp DA, Rajagopal KR, Smolinski PJ, Borovetz HS (1995) Identification of elastic properties of homogeneous, orthotropic vascular segments in distension. J Biomech 28(5):501–512

    Google Scholar 

  145. Vossoughi J, Hedjazi Z, Borris FS (1993) Intimal residual stress and strain in large arteries. In: BED—ASME summer bioengineering conference proceedings, vol 24. ASME, New York, pp 434–437

    Google Scholar 

  146. Wang C, Garcia M, Lu X, Lanir Y, Kassab GS (2006) Three-dimensional mechanical properties of porcine coronary arteries: a validated two-layer model. Am J Physiol Heart Circ Physiol 291(3):H1200–H1209

    Google Scholar 

  147. Watton PN, Hill NA, Heil M (2004) A mathematical model for the growth of the abdominal aortic aneurysm. Biomech Model Mechanobiol 3(2):98–113

    Google Scholar 

  148. Westerhof N, Elzinga G, Sipkema P (1971) An artificial arterial system for pumping hearts. J Appl Physiol 31(5):776–781

    Google Scholar 

  149. Wolinsky H, Glagov S (1964) Structural basis for the static mechanical properties of the aortic media. Circ Res 14:400–413

    Google Scholar 

  150. Wolinsky H, Glagov S (1967) A lamellar unit of aortic medial structure and function in mammals. Circ Res 20:99–111

    Google Scholar 

  151. Wu X, Levenston ME, Chaikof EL (2006) A constitutive model for protein-based materials. Biomaterials 2(30):5315–5325

    Google Scholar 

  152. Wulandana R, Robertson AM (2005) An inelastic multi-mechanism constitutive equation for cerebral arterial tissue. Biomech Model Mechanobiol 4(4):235–248

    Google Scholar 

  153. Yin FC, Chan CC, Judd RM (1996) Compressibility of perfused passive myocardium. Am J Physiol Heart Circ Physiol 271(5):H1864–H1870

    Google Scholar 

  154. Younis HF, Kaazempur-Mofrad MR, Chan RC, Isasi AG, Hinton DP, Chau AH, Kim LA, Kamm RD (2004) Hemodynamics and wall mechanics in human carotid bifurcation and its consequences for atherogenesis: investigation of inter-individual variation. Biomech Model Mechanobiol 3(1):17–32

    Google Scholar 

  155. Zeidler E (1990) Nonlinear functional analysis and its applications, vol II/B: nonlinear monotone operators. Springer, New York

    Google Scholar 

  156. Zeidler E (1997) Nonlinear functional analysis and its applications, vol IV: applications to mathematical physics. Springer, New York

    Google Scholar 

  157. Zhang Y, Dunn ML, Drexler ES, McCowan CN, Slifka AJ, Ivy DD, Shandas R (2005) A microstructural hyperelastic model of pulmonary arteries under normo- and hypertensive conditions. Ann Biomed Eng 33(8):1042–1052

    Google Scholar 

  158. Zienkiewicz OC, Taylor RL (2005) The finite element method, 6th edn. Elsevier Butterwoth–Heineman, Oxford

    MATH  Google Scholar 

  159. Zulliger MA, Rachev A, Stergiopulos N (2004) A constitutive formulation of arterial mechanics including vascular smooth muscle tone. Am J Physiol Heart Circ Physiol 287(3):H1335–H1343

    Google Scholar 

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Kalita, P., Schaefer, R. Mechanical Models of Artery Walls. Arch Computat Methods Eng 15, 1–36 (2008). https://doi.org/10.1007/s11831-007-9015-5

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