A nonlinear, anisotropic and axisymmetric model for balloon angioplasty

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Volumn 461, Issue 2056, 2005, Pages 1097-1128

  Eftaxiopoulos, Dimitrios A ^a   Atkinson, Colin ^b  

^a NATIONAL TECHNICAL UNIVERSITY OF ATHENS   (Greece)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Anisotropy; Artery; Atherosclerotic plaque; Axial symmetry; Balloon; Nonlinear elasticity

Indexed keywords

EID: 26944489624     PISSN: 13645021     EISSN: 14712946     Source Type: Journal    
DOI: 10.1098/rspa.2004.1419     Document Type: Article

References (25)

1. Atkinson, C. & Peltier, B. 1993 The finite deformation of a reinforced packer; membrane theory. J. Eng. Math. 27, 443-454.
2. Atkinson, C., Desroches, J., Eftaxiopoulos, D. A. & Thiercelin, M. 2001 Wellbore stresses induced by the nonlinear deformation of an inflatable packer. J. Engng. Math. 41, 305-327.
3. Gourisankaran, V. & Sharma, M. G. 2000 The finite element analysis of stresses in atherosclerotic arteries during balloon angioplasty. Crit. Rev. Biomed. Eng. 28(1&2), 47-51.
4. Green, A. E. & Adkins, J. E. 1970 Large Elastic Deformation, 2nd edn. Oxford: Clarendon Press.
5. Hart, V. G. & Shi, J. 1991 Joined dissimilar isotropic elastic cylindrical membranes under internal pressure and longitudinal tension. Q. J. Mech. Appl. Math. 44(4), 581-600.
6. Hart, V. G. & Shi, J. 1992 Joined dissimilar thin elastic tubes containing steady perfect flow. Z. Angew. Math. Phys. 43, 1038-1054.
7. Hart, V. G. & Shi, J. 1993 Joined dissimilar orthotropic elastic cylindrical membranes under internal pressure and longitudinal tension. J. Aust. Math. Soc. Ser. B 34, 296-317.
8. Hart, V. G. & Shi, J. 1995a Effects of initial deformation in thin tubes on wave reflection and transmission at mechanical mismatch. J. Sound Vibr. 188(4), 461-478.
9. Hart, V. G. & Shi, J. 1995b Governing equations for wave propagation in prestressed joined dissimilar elastic tubes containing fluid flow: with an example for a tapered section. Int. J. Eng. Sci. 33(8), 1121-1138.
10. Haughton, D. M. & McKay, B. A. 1997 Inflation of joined dissimilar elastic tubes. Q. J. Mech. Appl. Math. 50(1), 69-83.
11. Hayashi, K. & Imai, Y. 1997 Tensile property of atheromatous plaque and an analysis of stress in atherosclerotic wall. J. Biomech. 30(6), 573-579.
12. Holzapfel, G. A., Stadler, M. & Schulze-Bauer, C. A. J. 2002 A layer-specific three dimensional model for the simulation of balloon angioplasty using magnetic resonance imaging and mechanical testing. Ann. Biomed. Eng. 30, 753-767.
13. Kydoniefs, A. D. 1969 Finite axisymmetric deformations of an initially cylindrical elastic membrane enclosing a rigid body. Q. J. Mech. Appl. Math. 22, 319-331.
14. Kydoniefs, A. D. 1970 Finite axisymmetric deformations of an initial cylindrical membrane reinforced with inextensible cords. Q. J. Mech. Appl. Math. 23, 481-488.
15. Kydoniefs, A. D. & Spencer, A. J. M. 1969 Finite axisymmetric deformations of an initially cylindrical elastic membrane. Q. J. Mech. Appl. Math. 22, 87-95.
16. Lee, R. T. 2000 Atherosclerotic lesion mechanics versus biology. Z. Kardiol. 89(Suppl. 2), II/81-II/84.
17. Loree, H. M., Grodginsky, A. J., Park, S. Y., Gibson, L. J. & Lee, R. T. 1994 Static circumferential tangential modulus of human atherosclerotic tissue. J. Biomech. 27(2), 195-204.
18. Medynsky, A. O., Holdsworth, D. W., Sherebrin, M. H., Rankin, R. N. & Roach, M. R. 1998 Elastic response of human iliac arteries in-vitro to balloon angioplasty using high-resolution CT. J. Biomech. 31, 747-751.
19. Oh, S., Kleinberger, M. & McElhaney, J. H. 1994 Finite-element analysis of balloon angioplasty. Med. Biol. Eng. Comp. 32(4 Suppl.), S108-S114.
20. Pipkin, A. C. 1968 Integration of an equation in membrane theory. Z. Angew. Math. Phys. 19, 818-819.
21. Press, W. H., Teukolsky, S. A., Wetterling, W. T. & Flannery, B. P. 1994 Numerical recipes in C: the art of scientific computing, 2nd edn. Cambridge: Cambridge University Press.
22. Spencer, A. J. M. 1970 The static theory of finite elasticity. J. Inst. Math. Appl. 6, 164-200.
23. Spencer, A. J. M. 1980 Continuum Mechanics. New York: Longman.
24. Topoleski, L. D. T. & Salunke, N. V. 2000 Mechanical behavior of calcified plaques: a summary of compression an stress-relaxation experiments. Z. Kardiol. 89(Suppl. 2), II/85-II/91.
25. Vaishnav, R. N. 1980 Mathematical characterization of the nonlinear rheological behavior of the vascular tissue. Biorheology 17, 219-226.