An inelastic multi-mechanism constitutive equation for cerebral arterial tissue

Biomechanics and Modeling in Mechanobiology

Volumn 4, Issue 4, 2005, Pages 235-248

  Wulandana, R ^a   Robertson, A M ^a  

^a University of Pittsburgh   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BIODEGRADATION; BLOOD VESSELS; COLLAGEN; DEFORMATION; HISTOLOGY; TISSUE;

ANEURYSM; ARTERIAL BIFURCATIONS; DUAL-MECHANISM; ELASTIC DEFORMATIONS; INTRACRANIAL ANEURYSMS (ICA);

BIOMECHANICS;

ANIMAL; ARTICLE; BIOLOGICAL MODEL; BLOOD FLOW VELOCITY; BLOOD PRESSURE; BRAIN ARTERY; COMPUTER SIMULATION; ELASTICITY; HUMAN; MECHANOTRANSDUCTION; PHYSIOLOGY; VASCULAR RESISTANCE; VISCOSITY;

ANIMALS; BLOOD FLOW VELOCITY; BLOOD PRESSURE; CEREBRAL ARTERIES; COMPUTER SIMULATION; ELASTICITY; HUMANS; MECHANOTRANSDUCTION, CELLULAR; MODELS, CARDIOVASCULAR; VASCULAR RESISTANCE; VISCOSITY;

EID: 28344446195     PISSN: 16177959     EISSN: 16822978     Source Type: Journal    
DOI: 10.1007/s10237-005-0004-z     Document Type: Article

References (74)

1. Allcock, JM, Canham PB (1976) Angiographic study of the growth of intracranial aneurysms. J Neurosurg 45:617-621
2. Barrett JM, Hooydonk JEV, Boehm FH (1982) Pregnancy-related rupture of arterial aneurysm. Obstetrical and Gynecological Survey 37(9):557-566
3. Björkesten GAF, Troup H (1962) Changes in the size of intracranial arterial aneurysms. J Neurosurg 19:583-588
4. Broderick JP, Brott TG, Duldner JE, Tomsick T, Leach A (1994) Initial and reccurent bleeding are the major causes of death following subarachnoid hemorrhage. Stroke 25:1342-1347
5. Brown AM (2001) A step-by-step guide to nonlinear regression analysis of experimental data using a microsoft excel spreadsheet. Computer Methods and Programs in Biomedicine 65:191-200
6. Busby DE, Burton AC (1965) The effect of age on the elasticity of the major brain arteries. Can J Physiol Pharmacol 43:185-202
7. Cajander S, Hassler O (1976) Enzymatic destruction of the elastic lamella at the mouth of cerebral berry aneurysm? An ultrastructural study with special regard to the elastic tissue. Acta Neruol Scand 53:171-181
8. Canham P, Whittaker P, Barwick SE, Schwab ME (1991) Effect of pressure on circumferential order of adventitial collagen in human brain arteries. Can J Physiol Pharmacol 70:296-305
9. Canham PB, Ferguson GG (1985) A mathematical model for the mechanics of saccular aneurysms. Neurosurgery 17:291-295
10. Carew TE, Vaishnav RN, Patel DJ (1968) Compressibilty of the arterial wall. Circulation Research 23:61-68
11. Chalupnik J, Daly CH, Merchant HC (1973) Final report on contract no. NIH-69-2232 material properties of cerebral blood vessels. Technical Report ME 71-11, The University of Washington, Seattle, Washington
12. Chuong CJ, Fung YC (1984) Compressibility and constitutive equation of the arterial wall in radial compression experiments. J Biomech 17:35-40
13. Cope DA, Roach MR (1975) A scanning electron microscope study of human cerebral arteries. Can J Physiol Pharmacol 53:651-659
14. Delfino A, Stergiopulos N Jr, Moore JE, Meister JJ (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
15. Demiray H, Vito RP (1976) Large deformation analysis of soft biomaterials. Int J Engrng Sci 14:789-793
16. Ebhardt G, Wüllenweber R, Cervós-Navaro J (1976) The Cerebral Vessel Wall, chapter The Ultrastructure of the Aneurysmatic Vessel Wall, Raven Press pp 67-74
17. Finlay HM, McCullough L, Canham PB (1995) Three-dimensional collagen organization of human brain arteries at different transmural pressures. J Vase Res 32:301-312
18. Forbus WD (1930) On the origin of miliary aneurysms of the superficial cerebral arteries. Bulletin of the Johns Hopkins Hospital 47(5):239-284
19. Foutrakis GN, Yonas H, Sclabassi RJ (1999) Saccular aneurysm formation in curved and bifurcating arteries. Am J Neuroradiology 20:1309-1317
20. Green A, Adkins J (1960) Large Elastic Deformations Oxford University Press, Oxford
21. Green JF, Jackman AP (1979) Mechanism of the increased vascular capacity produced by mild perfusion hypothermia in the dog. Circ Res 44:411-419
22. Hademenos GJ, Massoud T, Valentino DJ, Duckwiler G, Viñuela F (1994) A nonlinear mathematical model for the development and rupture of intracranial saccular aneurysms. Neurol Res 16:376-384
23. Hayashi K, Handa H, Nagasawa S, Okumura A, Moritake K (1980a) Stiffness and elastic behavior of human intracranial and extracranial arteries. J Biomech 13:175-184
24. Hayashi K, Nagasawa S, Naruo Y, Okumura A, Moritako K, Handa H (1980b) Mechanical properties of human cerebral arteries. Biorheology 17:211-218
25. Huffman AS, Grande LA, Park JB (1977) Sequential enzymolysis of human aorta and resultant stress-strain behavior. Biomater Med Devices Artif Organs 5(2): 121-145
26. Holzapfel GA, Gasser TC, Ogden RW (2000) A new constitutive framework for arterial wall mechanics and a comparative study of material models. J Elasticity 61:1-48
27. Humphrey JD, Yin FC (1989) Biomechanical experiments on excised myocardium: theoretical considerations. J Biomech 22:377-383
28. Hung EJ, Botwin MR (1975) Mechanics of rupture of cerebral saccular aneurysms. J Biomech 8:385-392
29. Huntley HE, Wineman AS, Rajagopal KR (1996) Chemorheologial relaxation, residual stress, and permanent set arising in radial deformation of elastomeric hollow spheres. Math Mech Solids 1:267-299
30. Ingall TJ, Whisnant JP, Wiebers DO, O'Fallon WM (1989) Has there been a decline in subarachnoid hemorrhage mortality? Stroke 20:718-724
31. Johnson GA, Rajagopal KR, Woo SLY (1992) A single integral finite strain (SIFS) model of ligaments and tendons. Adv Bioeng 6:11-23
32. Johnson GA, Livesay GA, Woo SL-Y, Rajagopal KR (1996) A single integral finite strain viscoelastic model of ligaments and tendons. ASME J Biomech Eng 118:221-226
33. Juvela S, Poussa K, Porras M (2001) Factors affecting formation and growth of intracranial aneurysms - a long-term follow-up study. Stroke 32:485-491
34. Kamath S (1981) Observations on the length and diameter of vessels forming the circle of Willis. J Anat 133(3):412-423
35. Krex D, Schackert H, Schackert G (2001) Genesis of cerebral aneurysms - An update. Acta Neurochir (Wien) 143:429-449
36. Kyriacou SK, Humphrey JD (1996) Influence of size, shape and properties on the mechanics of axisymmetric saccular aneurysms. J Biomech 29:1015-1022
37. Lang ER, Kidd M (1963) Electron microscopy of human cerebral aneurysms. J Neurosurg 20:554-562
38. Lapczyk I, Rajagopal KR, Srinivasa AR (1998) Deformation twinning during impact - numerical calculations using a constitutive theory based on multiple natural configurations. Comput Mech 21:20-27
39. Naghdi PM (1984) Handbuch der Physik. In: Truesdell C (ed) Mechanics of solids, vol II. The theory of shells and plates. Springer, Berlin Heidelberg New York, pp 425-640
40. Naghdi PM, Tang PY (1977) Large deformation possible in every isotropic elastic membrane. Philos Trans Roy Soc London Ser A 287(1341):145-187
41. Orlandini GE, Ruggiero C, Orlandini SZ, Gulisano M (1985) Blood vessels size of arteriosus cerebri (circle of Willis): a statistical research on 100 human subjects. Acta Anat 123:72-76
42. Rajagopal KR, Srinivasa AR (1995) On the inelastic behavior of solids. Part I: Twinning. Int J Plasticity 11(6):653-678
43. Rajagopal KR, Srinivasa AR (1999) On the thermomechanics of shape memory wires. Z angew Math Phys 50:459-496
44. Rajagopal KR, Srinivasa AR (2000) A thermodynamic frame work for rate type fluid models. J Non-Newton Fluid Mech 88:207-227
45. Rajagopal KR, Srinivasa AR (2001) Modeling anisotropic fluids within the framework of bodies with multiple natural configurations. J Non-Newtonion Fluid Mech 99:109-124
46. Rajagopal KR, Wineman AS (1992) A constitutive equation for non-linear solids which undergo deformation induced microstructural changes. Int J Plasticity 8:385-395
47. Ratechenson R, Wirth F (1995) Concepts in neurosurgery. Ruptured cerebral aneurysms: perioperative management. Williams and Wilkins, Baltimore
48. Rhodin JAG (1979) Architecture of the vessel wall. In: Berne RM, Sperelakis N (eds) Vascular smooth muscle, vol 2 of Handbook of physiology, section 2: The Cardiovascular System. American Physiological Society, Baltimore, pp 1-31
49. Roach MR, Burton AC (1957) The reason for the shape of the distensibility curves of arteries. Can J Biochem Physiol 35:681-690
50. Ryan JM, Humphrey JD (1999) Finite element based predictions of preferred material symmetries in saccular aneurysms. Ann Biomed Eng 27:641-647
51. Sahs AL (1966) Observations on the pathology of saccular aneurysms. J Neurosurg 24:792-806
52. Samila ZJ, Carter SA (1981) The effect of age on the unfolding of elastin lamellae and collagen fibers with stretch in human carotid arteries. Can J Physiol Pharmacol 59:1050-1057
53. Sarwar M, Batnitzky S, Schecter MM, Liebeskind A, Zimmer AE (1976) Growing intracranial aneurysms. Radiology 120:603-607
54. Scanarini M, Mingrino S, Giordano R, Baroni A (1978) Histological and ultrastructural study of intracranial saccular aneurysmal wall. Acta Neurochirurgica 43:171-182
55. Scott S, Ferguson GG, Roach MR (1972) Comparison of the elastic properties of human intracranial arteries and aneurysms. Can J Physiol Pharmacol 50:328-332
56. Shah AD, Humphrey JD (1999) Finite strain elastodynamics of intracranial saccular aneurysms. J Biomech 32:593-599
57. Smith JFH, Canham PB, Starkey J (1977) Orientation of collagen in the tunica adventitia of the human cerebral artery measured with polarized light and the universal stage. J Ultrastruc Res 77:133-145
58. Stehbens WE (1963) Histopathology of cerebral aneurysms. Arch Neurol 8:272-285
59. Stehbens WE (1972) Pathology of the cerebral blood vessels. Structure and pathophysiology. C.V. Mosby
60. Stehbens WE (1989) Etiology of intracranial berry aneurysms. J Neurosurg 70:823-831
61. Sugai M, Shoji M (1968) Pathogenesis of so-called congenital aneurysms of the brain. Acta Path Jpn 18(2):139-160
62. Tobolsky A, Prettyman I, Dillon J (1944) Stress relaxation of natural and synthetic rubber stocks. J Appl Phys 15:380-395
63. Tóth M, Nádasy G, Nyáry I, Kerényi T, Monos E (2000) Are there systemic changes in the arterial biomechanics of intracranial aneurysm patients? Eur J Physiol 439:573-578
64. Truesdell C, Noll W (1992) The non-linear field theories of mechanics, 2nd edn. Springer, Berlin Heidelberg New York
65. Uchida M (1974) Electron microscopal studies on the arteries of brain basis II. Saccular aneurysm in rabbit and human cases. Kumamoto Med J 27(3): 150-169
66. Vaishnav RN (1980) Mathematical characterization of the nonlinear rheological behavior of the vascular tissue. Biorheology 17(3):219-226
67. Watton PN, Hill NA, Heil M (2004) A mathematical model for the growth of the abdominal aortic aneurysm. Biomech Model Mechanobiol 3:98-113
68. Wineman AS, Huntley HE (1994) Numerical simulation of the effect of damaged induced softening on the inflation of a circular rubber membrane. Int J Solids Struct 31(23):3295-3313
69. Wineman AS, Rajagopal KR (1990) On a constitutive theory for materials undergoing microstructural changes. Arch Mech 42(1):53-75
70. Wulandana R (2003) A nonlinear and inelastic constitutive equation for human cerebral arterial and aneurysm walls. PhD Thesis, University of Pittsburgh
71. Wulandana R, Robertson AM (2001) A model of early stage aneurysm development based on an inelastic multi-mechanism constitutive equation. In: BED-Vol. 50, ASME 2001 Bioengineering Conference, pp 419-420
72. Wulandana R, Robertson AM (2005) A multi-mechanism constitutive equations for modeling aneurysm development including: collagen recruitment, elastin failure, collagen degradation and collagen synthesis. In: Proceedings of the ASME 2005 Summer Bioengineering Conference, Vail, CO
73. Yamaki T, Yoshino E, Higuchi T (1986) Rapidly growing aneurysm. Surg Neurol 26:301-305
74. Yong-Zhong G, van Alphen HAM (1990) Pathogenesis and histopathology of saccular aneurysms: review of the literature. Neurol Res 12:249-255