Computer methods in membrane biomechanics

Computer Methods in Biomechanics and Biomedical Engineering

Volumn 1, Issue 3, 1998, Pages 171-210

  Humphrey, J D ^a,b  

^a University of Marylandw Baltimore County   (United States)

^b TEXAS A AND M UNIVERSITY   (United States)

Author keywords

Aneurysms; Cell mechanics; Elastodynamics; Experimental methods; Finite elements; Finite strains; Instabilities; Pericardium; Pleura; Pseudoelasticity; Skin; Wrinkling

Indexed keywords

ANEURYSMS; CELL MECHANICS; ELASTO-DYNAMICS; EXPERIMENTAL METHODS; FINITE ELEMENT; FINITE STRAIN; PERICARDIUM; PLEURA; PSEUDOELASTICITY; WRINKLING;

ELASTICITY; INITIAL VALUE PROBLEMS; SKIN; STABILITY;

BIOMECHANICS;

EID: 0001576351     PISSN: 10255842     EISSN: 14768259     Source Type: Journal    
DOI: 10.1080/01495739808936701     Document Type: Review

References (175)

1. Fung. Y. C. Biomechanics: Mcchanical Properties of Living Tissues (Springer verlag. NY, 1993), 2nd edition.
2. Love, A. E. H. A Treatise on the Mathematical Theory of Elasticity (Dover, NY. 1944). 4th edition, Chap. XXIV, pp.553-613.
3. Green. A. E. and Zcrna, W. Theoretical Elasticity (Oxford University Press, Oxford, 1968), Chaps 10-15, pp. 373-433.
4. Kraus, H. Thin Elastic Shells (John Wiley and Sons, NY, 1967).
5. Green, A. E. and Adkins, J. E. Large Elastic Deformations (Clarendon Press, Oxford. 1970), Chap IV, 133-173.
6. Libai. A. and Simmonds. J. G. The Nonlinear Theory of Elastic Shells (Academic Press, New York. 1988),
7. Truesdell. C. and Noll. W. (1965). The nonlinear field theories of mechanics. In: Handbuch der Physik. llU3, (Fiugge, Sed), Springer-Verlag, Berlin.
8. Spencer, A. J. M. Continuum Mechanics (Longman Group, UK. 1980).
9. Pipkin. A. C. (1968). Integration of an equation in membrane theory. ZAMP, 19, 818-819.
10. Skalak, R., Rachev, A. and Tozeren, A. (1975). Stressstrain relations for membranes under finite deformations. Bulgarian Academy of Sciences: Biomechanics, 2, 24-29.
11. Stcigmann. D. J. and Pipkin, A. C. (1989). Wrinkling of pressurized membranes. ASME Journal of Applied Mechanics, 56, 624-628.
12. Humphrey, J. D., Strumpf. R. K. and Yin. F. C. P. (1992). A constitutive theory for biomembranes: Application to epicardial mechanics. ASME Journal of Biomechanical Engineering, 114, 461-466.
13. Rivlin. R. S. and Saunders, D. W. (1951). Large elastic deformations of isotropic materials. VII Experiments on the deformation of rubber. Philosophical Transactions of the Royal Society, A243, 251-288.
14. Humphrey. J. D., Strumpf, R. K. and Yin. F. C. P. (1990). Biaxial mechanical behaviorof excised ventricular epicardium. American Journal of Physiology. 259. H101-HI08.
15. Lanir, Y. and Fung, Y. C. (1974). Two-dimensional mechanical properties of rabbit skin. II. Experimental results. Journal of Biomechanics, 7, 171-182.
16. Humphrey. J. D., Vawter. D. L. and Vito, R. P. (1987). Pseudoelasticity of excised visceral pleura. ASME Journal of Biomechanical Engineering, 109, 115-120.
17. Chew. P. H., Yin. F. C. P. and Zeger. S. L. (1986). Biaxial stress-strain properties of canine pericardium. Journal of Molecular and Cellular Cardiology, 18,567-578.
18. Kang, T., Humphrey. J. D. and Yin. F. C. P. (1996). Comparison of the biaxial mechanical properties of excised endocardium and epicardium. American Journal of Physiology. 270, H2169-H2176.
19. Hildebrandt, J., Fukaye. H. and Martin, C. J. (1969). Stress-strain relations of tissue sheets undergoing uniform two-dimensional stretch. Journal of Applied Physiology, 27, 758-762.
20. Ligas, J. R., Primiano. F. P. and Saidel. G. M. (1984). Static mechanics of excised whole lung: Pleural mechanics. Annals of Biomedical Engineering. 12, 437-448.
21. Kriewall, T. J., Akkas. N., Bylski. D. I., Melvin, J. W. and Work. B. A. (1983). Mechanical behavior of fetal dura mater under large axisymmetric inflation. ASME Journal of Biomechanical Engineering. 105, 71-76.
22. Miller, C. E., Lavery, J. P. and Donnelly, T. A, (1979). Determination of clastic parameters for human fetal membranes. Journal of Rheology. 23, 57-78.
23. Hsu, F. P. K., Schwab, C., Rigamonti. D. and Humphrey. J. D. (1994). Identification of response functions for nonlinear membranes via axisymmetric inflation tests: Implications for biomechanics. International Journal of Solids and Structures. 31, 3375-3386.
24. Evans. E. A. and Skalak, R. (1980). Mechanics and Thermodynamics of Biornembrunes (eRe Press. Buco Raton).
25. Sato, M., Theret, D. P., Wheeler. L. T., Ohshima. N. and Nerem. R. M. (1990). Application of the micropipette technique to the measurement of cultured porcine aortic endothelial cell viscoelastic properties. ASME Journal of Biomechanical Engineering. 112,263-268.
26. Hsu. F. P. K., Liu. A. M. c., Downs I., Rigarnonti, D. and Humphrey. J. D. (1995). A triplane video-based experimental system for studying axisyrnrnerrically inflated biomembranes. IEEE Transactions for Biomedical Engineering. 42, 442-450.
27. Humphrey, J. D. and Kyriacou, S. K. (1996). The usc of Laplace's equation in aneurysm mechanics. Neurological Research, 18, 204-208.
28. Bylski, D. I., Kriewall, T. J., Akkas, N. and Melvin, J. W. (1986). Mechanical behavior of fetal dura mater under large deformation biaxial tension. Journal of Biomechanics, 19, 19-26.
29. Fulton, J. P. and Simmonds, J. G. (1986). Large deformations under vertical edge loads of annular membranes with various strain energy densities. International Journal of Non-Linear Mechanics, 21, 257-267,
30. Tezduyar, T. E., Wheeler. L. T. and Gruux. L. (1987). Finite deformation of a circular elastic membrane containing a concentric rigid inclusion. International Journal of Non-Linear Mechanics, 22, 61-72.
31. Yongxiang. G. and Jisheng. L. (1994). The study on mechanical parameters of finite deformation of membranes. ASME Journal of Applied Mechanics, 61, 202-204.
32. Kyrincou. S. K., Shah, A. D. and Humphrey. J. D. (1997). Inverse finite element characterization of nonlinear hyperelastic membranes. ASME Journal of Applied Mechanics, 64, 257-262.
33. Wineman, A., Wilson, D. and Melvin, J. W. (1979). Material identification of soft tissue using membrane inflation. Journal of Biomechanics. 12, 841-850.
34. Yin. F. C. P., Chew, P. H. and Zeger, S. L. (1986). An approach to quantification o~ biaxial stress-strain data. Journal of Biomechanics, 19,27-37.
35. Humphrey, J. D., Strumpf. R. K. and Yin. F. C. P. (1990). Determination of a constitutive relation for passive myocardium: II Parameter estimation. ASME Journal of Biomechanical Engineering, 112, 340-346.
36. Pipkin, A. C. (1986). The relaxed energy density for isotropic membranes. IMA Journal of Applied Mathematics, 36, 85-99.
37. Treloar, L. R. G. (1944). Stress-strain data for vulcanized rubber under various types of deformations. Transactions of the Faraday Society. 40, 59-70.
38. Humphrey, J. D., Vawter, D. L. and Vito, R. P. (1986). Mechanical behavior of excised canine visceral pleura. Annals of Biomedical Engineering. 14, 451-466.
39. Nielsen. P. M. F., Hunter, P. J. and Smaill, B. H. (1991). Biaxial testing of membrane biornaterials: Testing equipment and procedures. ASME Journal of Biomechanical Engineering. 113,295-300.
40. Humphrey, J. D., Vawter, D. L. and ViIO, R. P. (1987). Quantification of strains in biaxially tested soft tissues. Journal of Biomechanics. 20, 59-65.
41. Downs, J., Halperin, H. R., Humphrey. J. D. and Yin, F. C. P. (1990). An improved video-based computer tracking system for soft biomaterials testing. IEEE Transactions for Biomedical Engineering, 37, 903-907.
42. Xu, P. and Mark J. E. (1990). Biaxial extension studies using inflation of sheets of unimodal model networks. Rubber Chemistry and Technology. 63, 276-284.
43. Ling, Y., Engel, P. A., Brodskey, W. L. and Guo, Y. (1993). Finding the constitutive relation for a specific elastomer. ASME Journal of Electronic Packaging. 115, 329-336.
44. Chew, P. H., Humphrey, J. D. and Yin, F. C. P. (1993). Regional finite deformations of the in-situ canine pericardium. American Journal of Physiology. 264. H97-HI03.
45. McCulloch, A. D., Smaill, B. H. and Hunter. P. J. (1987). Left ventricular epicardial deformation in isolated arrested dog heart. American Journal of Physiology, 252. H233-24 I.
46. Woods. R. H. (1892). A few applications of a physical theorem to membranes in the human body in a state of tension. Journal of Anatomy and Physiology, 26, 362-370.
47. Bogen, D. K. and McMahon, T. A. (1979). Do cardiac aneurysms blowout? Biophysical Journal. 27, 301-316.
48. Early. C. B. and Fink. L. H. (1976). Some fundamental applications of the law of Laplace in neurosurgery. Surgical Neurology, 6, 185-189.
49. Canham, P. B. and Ferguson. G. G. (1985). A mathematical model for the mechanics of saccular aneurysms. Neurosurgery. 17,291-295.
50. Vito. R. P. (1979). The role of the pericardium in cardiac mechanics. Journal of Biomechanics, 12, 587-592.
51. Shivakumar, P. J.J., Man. C. S. and Rabkin, S. W. (1989). Modelling of the heart and pericardium at end-diastole, Journal of Biomechanics. 22, 201-209.
52. Humphrey, J. D. (1987). A possible role of the pleura in lung mechanics. Journal of Biomechanics, 20, 773-777.
53. Fung, Y. C. and Tong, P. (1968). Theory of the sphering of red blood cells. Journal of Biophysics, 8, 175-198.
54. Regnier, C. H., Kolsky, H., Richardson, P. D., Ghoniern, G. M. (1983). The elastic behavior of the urinary bladder for large deformations. Journal of Biomechanics. 16,915-922.
55. Cahane, M. and Bartov, E. (1992). Axial length and scleral thickness effect on susceptibility to glaucomatous damage: A theoretical model implementing Laplace's law. Opthal Research, 24, 280-284.
56. Noveroske, R. J. (1979). Two applications of the law of Laplace to obstetrics. Journal of the Indiana State Medical Association. 72, 416-417.
57. Alexander, H. (1968). A constitutive relation for rubberlike materials. International Journal of Engineering Science, 6, 549-563.
58. Alexander. H. (1971). Tensile instability of initially spherical balloons, International Journal of Engineering Science, 9, 151-162.
59. Han-Smith. L. J. (1966). Elasticity parameters for finite deformations of rubber-like materials. ZAMP, 17,608-626.
60. Johnson, M. A. and Beatty. M. F. (1995). The Mullins effect in equibiaxial extension and its influence on the inflation of a balloon. International Journal of Engineering Science. 33, 221-245.
61. Treloar, L. R. G. (1975). The Physics of Rubber Elasticity (Clarendon Press. Oxford). 3rd edition.
62. Wong, J. S. K. and Shield, R, T. (1980). The stability of a cylindrical el esric membrane of biological tissue and the effect of internal fluid flow. Ingenieur Archiv, 49, 393-412.
63. Kydoniefs, A. D. and Spencer, A. J. M. (1969). Finite axisymmetric deformations of an initially cylindrical elastic membrane. Quarterly Journal of Mechanics and Applied Mathematics, 22, 87-95.
64. Rivlin. R. S. and Thomas. A. G. (1951). Large elastic deformations of isotropic materials VIII. Strain distribution around a hole in a sheet. Philosophical Transactions of the Royal Society of London. A243, 289-298.
65. Adkins. J. E. and Rivlin, R. S. (1952). Large elastic deformationsof isotropic materials IX. The deformation of thin shells. Philosophical Transactions of the Royal Society of London. A244. 505-531.
66. Hart-Smith. L. J. and Crisp, J. D. C. (1967). Large elastic deformations of thin rubber membranes. International Journal of Engineering Science. 5, 1-24.
67. Vito. R. P., MacManus, R. K. and Bradley. E. (1981). The mechanics of pancreatic pseudocyst. Journal of Biomechanics. 14, 215-220.
68. Schmidt. L. R. and Carley, J. F. (1975). Biaxial stretching of heat-softened plastic sheets using an inflation technique. International Journal of Engineering Science, 13, 563-578.
69. Sugiv, A. (1990), lnflutiou ofan axisymmetric membrane: Stress analysis. ASME Journal of Applied Mechanics, 50, 682-6R7.
70. Klingbeil, W. W. and Shield. R. T. (1964). Some nurnerical investigations 011 empirical strain energy functions in the large axisymmetric extensions of rubber membranes. ZAMP. 15, 608-629.
71. Yang, W. H. and Feng, W. W. (1970). On axisymmetric deformations of nonlinear membranes. Journal of Applied Mechanics. 37, 1002-2001.
72. Feng, W. W. and Yang, W. H. (1973). On the contact problem of an inflated spherical nonlinear membrane. ASME Journal of Applied Mechanics, 40, 209-214.
73. Pujara. P. and Lardner, T. J. (1978). Deformations of elastic membranes-Effect of differentconstitutive relations. ZAMP, 29, 315-327.
74. Feng, W. W., Tielking. J. T. and Huang, P. (1974). The inflation and contact constraint of a rectangular Mooney membrane. ASME Journal of Applied Mechanics, 41, 979-984.
75. Fcng. W. W. and Huang. P. (1975). On the general contact problem of an inflated nonlinear plane membrane. International Journal of Solids and Structures. 11, 437-448.
76. Fcng. W. W. andTielking. J. T. (1976). Largeplanedeformations of rectangular elastic sheets. ZAMP, 27, 781-788.
77. Taber, L. A. (1984). Large deformation mechanics of the enucleated eyeball. ASME Journal of Biomecbanical Engineering. 106, 229-234.
78. Yang. W. H. and Lu, C. H. (1973). General deformations of nco-Hookcun membranes. ASME Journal of Applied Mechanics, 40, 7-12.
79. Wu, C. H. and Perng. D. Y. P. (1972). On the asymptotically spherical deformations of arbitrary membranes of revolution fixed along an edge and inflated by large pressures-a nonlinear boundary layer phenomenon. SIAM Journal of Applied Mathematics, 23, 133-152.
80. Nagdi. P. M. and Yang, P. Y., (1977). Large deformation possible in every isotropic elastic membrane. Philosophical Transactions of the Royal Society of London, A287, 145-187.
81. Yang, W. H. (1967). Stress concentration in a rubber sheet under axially symmetric stretching. ASME Journal of Applied Mechanics. 34, 942-946.
82. Verma, I. D. S. and Rana, O. H. (1978). Radial deformalion of a plane sheet containing a circular hole or inclusion. International Journal of Non-Linear Mechanics, 13, 223-232.
83. Varley, E. and Cumberbatch, E. (1980). Finite deformations of elastic materials surrounding cylindrical holes. Journal of Elasticity, 10, 341-405.
84. Danielsen, D. A. and Natarajan, S. (1975). Tension field theory and the stress in stretched skin. Journal of Biomechanics. 8, 135-142.
85. Wu, C. H. (1980). Sutures in stretched membranes. Quarterly of Applied Mathematics, 38, 109-I 19.
86. Odcn, J. T. (1972). Finite Elements of Nonlinear Continual (McGraw Hill, NY).
87. Fried, I. (1982). Finite element computation of large rubber membrane deformations. International Journal of Numerical Methods in Engineering, 18,653-660.
88. Charrier. J. M., Shrivastaba. S. and Wu, R. (1987). Free and constrained inflation of elastic membranes in relation to thermoforming-Axisymmetric problems. Journal of Strain Analysis, 22, 115-125.
89. Wriggers, P. and Taylor, R. L. (1990). A fully nonlinear axisymmetrical membrane element for rubber-like materials. Engineering Computing, 7, 303-310.
90. Tong, P. and Rosscuos, J. N. (1977). Finite Element Method (MIT Press, Cambridge MA).
91. Gruttman, F. and Taylor, R. L. (1992). Theory and finite element formulation of rubberlike membrane shells using principal stretches. International Journal for Numerical Methods in Engineering. 35, 1111-1126.
92. Kyriacou, S. K., Schwab, C. and Humphrey. J. D. (1996). Finiteelement analysis of nonlinearorthotropic hyperelastic membranes. Computational Mechanics, 18,269-278.
93. Charrier, J. M., Shrivasiaba. S. and Wu, R. (1989). Free and constrained inflation of elastic membranes in relation to thermoforming-Non-axisymmetric problems. Journal of Strain Analysis, 24, 55-74.
94. Zarnani. N. G., Wait, D. F. and Esteghamatiun, M. (1989). Status of the finite element method in the thermofonning process. International Journal for Numerical Methods in Engineering. 28, 2681-2693.
95. Neid, H. F., Taylor, C. A. and Delorenzi, H. G. (1990). Three-dimensional finite element simulation of thermoforming. Polymer Engineering and Science, 30, 1314-1322.
96. Schueler. B. A. and Rufenacht, D. A. (1993). Risk factors leading (0 cerebral arterial rupture by intravascular balloon. American Journal of Neuroradiology, 14, 1085-1093.
97. Humphrey, J. D. (1995). Arterial wall mechanics: Review and directions. Critical Reviews in Biomedical Engineering. 23, I-162.
98. Crisp. J. D. C. (1968). On the mechanical equilibrium states of cylindricalblood vessels. Microvascular Research, I, 35-57.
99. Corneliussen. A. H. and Shield, R. T. (1991). Finite defermarion of elastic membranes with applications to stability of an inflated and extended tube. Archives for Rational Mechanics and Analysis. 7, 273-304.
100. Benedict. R., Wineman. A. and Yang, W. H. (1979). The determination of limiting pressure in simultaneouselongation and inflation of nonlinear elastic tubes. International Journal of Solids and Structures, 15, 241-249.
101. Haugton, D. M. and Ogden. R. W. (1979). Bifurcation of inflated circularcylinders of elastic material underuniaxial loading. I. Membrane theory for thin-walled cylinders. Journal of the Mechanics and Physics of Solids, 27, 179-212.
102. Chater, E. and Hutchinson, J. W. (1984). On the propagation of bulges and buckles. Journal of Applied Mechanics, 51, 269-277.
103. Khayat. B. H., Derdouri, A. and Garcia-Rejon, A. (1992). Inflation of an elastic cylindrical membrane: Non-linear deformation and instability. International Journal of Solids and Structures. 29, 69-87.
104. Crisp. J. D. C. and Hart-Smith. L. J. (1971). Multi-lobed inflated membranes: Their stability under finite deformation. International Journal of Solids and Structures, 7, 843-861.
105. Akkas, N. (1990). Aneurysms as a biomechanical instability problem. In, Biomechanical Transport Processes (ed, F. Mosora). Plenum Press. pp. 303-31 I.
106. Beatty, M. F. (1987). Topics in finite elasticity: Hyoerelasticity of rubber elastomers and biological tissues-with examples. Applied Mechanics Reviews. 40, 1699-1734.
107. Wu, C. H. (1978). Nonlinear wrinkling of nonlinear membranes of revolution. ASME Journal of Applied Mechanics. 45, 533-538.
108. Steigmann. D. J. and Pipkin. A. C. (1989). Axisymmetric tension fields. Journal of Mathematics and Physics (ZAMP). 40, 526-542.
109. Steigmann. D. J. (1990). Tension field theory. Proceedings of the Royal Society of London. A429, 141-173.
110. Li, X. and Steigmann. D. J. (1993). Finite plane twist of an annular membrane. Quarterly Journal for Mechanics and Applied Mathematics, 46, 601-625.
111. Haughton. D. M. and McKay. B. A. (1996). Wrinkling of inflatedelastic cylindrical membranes under flexure. International Journal of Engineering Science, 13, 1531-1550.
112. Haseganu, E. M. and Steigrnann. D. J. (1994). Theoretical flexural response of a pressurized cylindrical membrane. International Journal of Solids and Structures, 31, 27-50.
113. Jenkins. C. H. and Leonard. J. W. (1991). Nonlinear dynamic response of membranes: State of the art. Applied Mechanics Reviews. 44, 319-328.
114. Jenkins. C. H. (1991). Nonlinear dynamic response of membranes: State of the art-update. Applied Mechanics Reviews. 44, S41-548.
115. Wang. C. C. (1965). On the radial oscillations of a spherical thin shell in the finite elasticity theory. Quarterly of Applied Mathematics, 23, 270-274.
116. Akkas, N. (1978). On the dynamic snap-out instability of inflated nonlinear spherical membranes. International Journal of Non-Linear Mechanics. 13, 177-183.
117. Mukherjee. K. and Chakraborty, S. K. (1985). Exact solution for large amplitude free and forced oscillation of a thin spherical shell. Joumal of Sound and Vibration, 100, 339-342.
118. Shah. A. D. and Humphrey. J. D. (1998). Finite strain elastodynamics of saccularaneurysms. Journal of Biomechanics (accepted).
119. Knowles, I. K. (1960). Large amplitude oscillations of a tube of incompressible elastic material. Quarterly of Applied Mathematics. 18, 71-78.
120. Knowles, J. K. (1962). On a class of oscillations in the finite-deformation theory of elasticity. ASME Journal of Applied Mechanics. 29, 283-286.
121. Rogers. C. and Baker. J. A. (1980). The finite elastodynamics of hyperelastic thin tubes. fnternational Journal of Non-Linear Mechanics. 15, 225-233.
122. Stamenovic. D. (1988). Equilibria of a pressurized cylindrical membrane with a non-monotonic pressure-volume characteristic. Quarterly Journal of MechanicsandApplied Mathematics, 41, 71-81.
123. Enhorning. G. (1977). Pulsating bubble technique for evaluating pulmonary surfactant. Journal of Applied Physiology, 43, 198-203.
124. Hall. S. B., Bermel. M. S., Ko. Y. T., Palmer, H. J., Enhornin, G. and Nolter. R. H. (1993). Approximations in the measurement of surface tension on the oscillating bubble surfactomerer. Journal of Applied Physiology. 75, 468-477.
125. Fung, Y. C. B. (1967). Elasticity of soft tissues in simple elongation. American Journal of Physiology, 213, 1532-1544.
126. Danielson. D. A. (1973). Human skin as an elastic membrane. Journal of Biomechanics. 6, 539-546.
127. Tong. P. and Fung, Y. C. (1976). The stress-strain relationship for the skin. Journal of Biomechanics. 9, 649-657.
128. Shoemaker. P. A., Schneider, D., Lee, M. C. and Fung, Y. C. (1986). A constitutive model for two-dimensional soft tissues and its application to experimental data. Journal of Biomechanics, 19, 695-702.
129. Larrabee. W. F. (1986). A finite element model of skin deformation. I Biomechanics of skin and soft tissue: A review. Laryngoscope. 96, 399-405.
130. Atkinson. C. (1981). On a possible theory for the design of tissue expanders. Quarterly Journal of Mechanics and Applied Mathematics. 41, 301-317.
131. Chuang. C. J., Sacks. M. S., Johnson. R. L. and Reynolds. R. (1991). On the anisotropy of the canine diaphragmatic central tendon. Journal of Biomechanics, 7, 563-576.
132. Lee. J. M., Haberer. S. A. and Boughner. D. R. (1989). The bovine pericardial xenograft: I. Effect of fixation in aldehydes without constraint on the tensile viscoelastic properties of bovine pericardium. Journal of Biomedical Materials Research. 23, 457-475.
133. Lee. J. M., Corrente, R. and Haberer. S. A. (1989). The bovine pericardial xenograft: II. Effect of tethering or pressurization during fixation on the tensile viscoelastic properties of bovine pericardium. Journal of Biomedical Materials Research. 23, 477-489.
134. Lee. J. M., Ku. M. and Haberer. S. A. (1989). The bovine pericardial xenograft: Ill. Effect of uniaxialand sequential biaxial stress during fixation on the tensile viscoelastic properties of bovine pericardium. Journal of Biomedical Materials Research. 23, 491-506.
135. Hildebrandt. J., Fukayu, H. and Martin. C. J. (1969). Simple uniaxial and uniform biaxial deformation of nearly isotropic incompressible bodies. Journal of Biophysics. 9, 781-791.
136. Weigner, A. W. and Bing. O. H. L. (1981). Mechanical andstructural correlates of canine pericardium. Circulation Research. 49, 807-814.
137. Lee. J. M. and Boughner. D. R. (1985). Mechanical properties of human pericardium. Circulation Research. 55, 475-481.
138. Nairnark, W. A., Lee. J. M., Limeback, H. and Cheung, D. T. (1992). Correlation of structure and viscoelastic properties in the pericardia of four mammalian species. American Journal of Physiology. 263. HI095-1106.
139. Lee, M. c., Lewinter, M. M., Freeman, G., Shabetai, R. and Fung. Y. C. (1985). Biaxial mechanical properties of the pericardium in normal and volume overload dogs. American Journal of Physiology, 249, H222-230.
140. Choi. H. S. and Vila. R. P. (1990). Two dimensional stress-strain relationship for canine pericardium, ASME Journal of Biomechanical Engineering, 112, 153-159.
141. Tyson, G. S., Maier. G. W., Olsen. C. O., Davis. J. W. and Rankin, J. S. (1984). Pericardia] influences on ventricular filling in the conscious dog, Circulation Research, 54, 173-184.
142. Mann. D., Lew. W., Ban-Hayashi. E., Shabetui. R., Waldman, L. K. and LeWinter, M. M. (1986). In vivo mechanical behavior of canine pericardium. American Journal of Physiology, 251. H349-356.
143. Humphrey, J. D. and Yin, F. C. P. (1988). Biaxial mechanical behavior of excised epicardium. ASME Journal of Biomcchanical Engineering, 110,349-351, (Erratum 111:227, 1989),
144. Oldmixon, E. H. and Hoppin. F. G. (1984). Comparison of amounts of collagen and clastic in pleura and parenchyma of dog lung. Journal of Applied Physiology, 56, 1383-1388.
145. von Hayek. H. (1960). The Human Lung (Hafner, NY).
146. Wilson, T. A. (1981). Mechanics of the pressure-volume curve of the lung. Annals of Biomedical Engineering, 9, 439-449.
147. Nagao, K. (1973). Experimental studies on mechanical properties of the visceral pleura. Nihon University Journal of Medicine. 15,307-327.
148. Hajii, M. A. (1978). Indentation of a membrane on an clastic half space. ASME Journal of Applied Mechanics, 45, 320-324.
149. Stamcnovic. D. (1984). Mechanical properties of the pleural membrane. Journal of Applied Physiology, 57, 1189-1194.
150. Elgcr, D. F., Hlackkeuer. D, M., Budwig, R. S. and Johansen, K. H. (1996). The influence of shape on the stresses in model abdominal aortic aneurysms. ASME Journal of Biomcchanical Engineering. 118, 326-332.
151. Shah, A. D., Harris, J. L., Kyriacou, S. K. and Humphrey, J. D. (1998). Further roles of geometry and properties in the mechanics of saccular aneurysms. Computer Methods in Hiomcchanics and Biomedical Engineering (accepted).
152. SCOll, S., Ferguson, G. G. and Roach, M. R. (1972). Comparison of the clastic properties of human intracranial arteries and aneurysms. Canadian Journal of Physiology and Pharmacology, 50, 328-332.
153. Kyrincou. S. K. and Humphrey, J. D. (1996). Influence of size, shape and properties on the mechanics ofaxisymmetric saccular aneurysms. Journal of Biomechanics, 29, 1015-1022.
154. Austin, G. M., Schievink, W. and Williams, R. (1989). Controlled pressure-volume factors in the enlargement of iruracranial saccular aneurysms. Neurosurgery. 24, 722-730.
155. Simkins, T. E. and Stchbcns, W. E. (1974). Vibrational behavior of arterial aneurysms. Letters in Applied Engineering Science I. 85-100.
156. Hung, E. J. N. and Botwin. M. R. (1975). Mechanics of rupture of cerebral saccular aneurysms. Journal of Biomechanics K, 385-392.
157. Sckhar, L. N. and Heros, R. C. (1981). Origin, growth and rupture of saccularaneurysms: A review. Neurosurgery. 8, 248-260.
158. Stchbcns, W. E. (1990). Pathology and pathogenesis of intracranial berry aneurysms. Neurological Research, 12, 29-34.
159. Zarda. P. R., Chien, S. and Skulak, R. (1977). Elastic deformations of red blood cells. Journal of Biomechanics, 10,211-221.
160. Skalak, R., Tozeren, A., Zarda. A. P. and Cbien, S. (1973). Strain energy function of red blood cell membranes. Biophysical Journal, 13, 245-264.
161. Chien, S., Sung, K. L. P., Skalak, R., Usami, S. and Tozeren, A. (1978). Theoretical and experimental studies on viscoelastic properties of erythrocyte membrane. Biophysical Journal. 24, 463-487.
162. Hochmuth, R, M. (1993). Measuring the mechanical propcrues of individual human blood cells. ASME Journal of Biomechanical Engineering, 15, 515-519.
163. Tran-Son-Tay. R., Sutera, S. P., Zahalak, G. I. and Rao, P. R. (1987). Membrane stress and internal pressure in a red blood cell freely suspended in a shear flow. Biophysical Journal, 51, 915-924.
164. Zahalak, G. I., Rao, P, R. and Sutera, S. P. (1987). Large deformations of a cylindrical liquid-filled membrane by a viscous shear flow. Journal of Fluid Mechanics. 179, 283-305.
165. Nerem, R. M. (1993). Hemodynamics and the vascular endothelium. ASME Journal of Biomechanical Engineering, 115, 510-514.
166. Fung, Y. C. and Liu, S. Q. (1993). Elementary mechanics of the endothelium of blood vessels. ASME Journal of Biomechanical Engineering, 15, 1-12.
167. Zahalak, G. I., McConnaughey, W. B. and Elson, E. L. (1990). Determination of cellular mechanical properties by cell poking, with an application to leukocytes. ASME Journal of Biomechanical Engineering, 112, 283-294.
168. Schrnid-Schonbein, G. W., Kosuwada. T., Skalak, R. and Chien, S. (1995). Membrane model of endothelial cells and leukocytes: A proposal for the origin of a cortical stress. ASME Journal of Biomechanical Engineering, 117, 171-178.
169. Dong, C; Skalak, R., Sung, K. L. P., Schmid-Schonbein, G. W., Chien, S. (1988). Passive Deformation analysis of human leukocytes. Journal of Biomechanical Engineering. 110,27-36.
170. Gorfien, S. F., Winston. F. K., Thibault, L. E. and Macarak, E. J, (1989), Effects of biaxial deformation on pulmonary artery endothelial cells. Journal of Cell Physiology, 139,492-500.
171. Williams, J. L., Chen, J. H. and Belloli, D. M. (1992). Strain fields on cell stressing devices employing clamped circularelastic diaphrams as substrates. ASME Journal of Biomeehanical Engineering, 114,377-384.
172. Gilbert, J. A., Weinhold, P. S., Banes, A. J., Link, G. W. and Jones, G. L. (1994). Strain profiles for circular cell culture plates containing flexible surfaces employed 10 mechanically deform cells in vitro. Journal of Biomechanics, 27, 1169-1177.
173. Barbee, K. A., Macarak, E. J. and Thibault, L. E. (1994), Strain measurements in cultured vascular smooth muscle cells subjected to mechanical deformation. Annals Biomedical Engineering, 22, 14-22.
174. Spence, R. D. and Wu, H. I. (1995). Plant cell wall elasticity III. A polymerelastic interpretation of inverse pressurevolume curves. J Theoretical Biology, 177, 59-65.
175. Cheng. L. Y. (1987). Deformation analyses in cell and developmental biology. Part I-Formal methodology. ASME Journal of Biornechanical Engineering, 109, 10-24.