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Intracranial Saccular Aneurysms

  • J. D. Humphrey
Part of the International Centre for Mechanical Sciences book series (CISM, volume 441)

Abstract

It has long been accepted that mechanical factors play a critical role in the natural history of intracranial saccular aneurysms — their pathogenesis, enlargement, and rupture. Nevertheless, until very recently, biomechanical analysis has been surprisingly scant. In this chapter, we see how nonlinear elasticity, membrane theory, nonlinear dynamics, and nonlinear finite element analyses can be used to increase our understanding of the mechanics of saccular aneurysms. Much has been learned, but much remains to be accomplished, particularly in the area of the mechanics of biological growth and remodeling. Hence, it is also hoped that this chapter will encourage new investigators to study the mechanics of aneurysms.

Keywords

Constitutive Relation Principal Curvature Stretch Ratio Saccular Aneurysm Membrane Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Akkas, N. (1990). Aneurysms as a biomechanical instability problem. In Mosora F., ed., Biomechanical Transport Processes. Plenum Press. 303–311.Google Scholar
  2. Austin, G. (1971). Biomathematical model of aneurysm of the Circle of Willis: The Duffing equation and some approximate solutions. Math. Biosci. 11:163–172.CrossRefMATHGoogle Scholar
  3. Austin, G.M., Schievink, W. and Williams, R. (1989). Controlled pressure-volume factors in the enlargement of intracranial saccular aneurysms. Neurosurg. 24:722–730.CrossRefGoogle Scholar
  4. Beatty, M.F. (1987). Topics in finite elasticity: Hyperelasticity of rubber, elastomers, and biological tissues — with examples. Appl. Mech. Rev. 40:1699–1734.CrossRefGoogle Scholar
  5. Bruno, G., Todor, R., Lewis, I. and Chyatte, D. (1998). Vascular extracellular matrix remodeling in cerebral aneurysms. J. Neurosurg. 89:431–440.CrossRefGoogle Scholar
  6. Canham, P.B. and Ferguson, G.G. (1985). A mathematical model for the mechanics of saccular aneurysms. Neurosurg. 17:291–295.CrossRefGoogle Scholar
  7. Canham, P.B., Finlay, H.M., Dixon, J.G. and Ferguson, S. (1991). Layered collagen fabric of cerebral aneurysms quantitatively assessed by the universal stage and polarized light microscope. Anat. Record 231:579–592.CrossRefGoogle Scholar
  8. Canham, P.B., Whittaker, P., Barwick, S.E. and Schwab, M.E. (1991). Effect on circumferential order of adventitial collagen in human brain arteries. Can. J. Physiol. Pharmacol. 70:296–305.CrossRefGoogle Scholar
  9. Canham, P.B., Finlay, H.M. and Tong S.Y. (1996). Stereological analysis of the layered structure of human intracranial aneurysms. J. Microsc. 183:170–180.CrossRefGoogle Scholar
  10. Canham, P.B., Finlay, H.M., Kiernan, J.A. and Ferguson, G.G. (1999). Layered structure of saccular aneurysms assessed by collagen birefringence. Neurol Res. 21:618–626.Google Scholar
  11. Chyatte, D., Reilly, J. and Tilson, M.D. (1990). Morphometric analysis of reticular and elastin fibers in the cerebral arteries of patients with intracranial aneurysms. Neurosurg. 26:939–942.CrossRefGoogle Scholar
  12. Cronin, J. (1973). Biomathematical model of aneurysm of the Circle of Willis: A qualitative analysis of the differential equation of Austin. Math. Biosci. 16:209–225.CrossRefMATHMathSciNetGoogle Scholar
  13. de la Monte, S.M., Moore, G.W., Monk, M.A. and Hutchins, G.M. (1985). Risk factors for development and rupture of intracranial berry aneurysms. Am. J. Med. 78:957–964.CrossRefGoogle Scholar
  14. Ferguson, G.G. (1972). Physical factors in the initiation, growth, and rupture of human intracranial aneurysms. J. Neurosurg. 37:666–677.CrossRefGoogle Scholar
  15. Ferguson, G.G. (1972). Direct measurement of mean and pulsatile blood pressure at operation in human intracranial saccular aneurysms. J. Neurosurg. 36:560–563.CrossRefGoogle Scholar
  16. Foutrakis, G.N., Yonas, H. and Sclabassi, R.J. (1994). Finite element methods in the simulation and analysis of intracranial blood flow: Saccular aneurysm formation in curved and bifurcating arteries. Tech. Rep. 6, University of Pittsburgh, Computational Neuroscience.Google Scholar
  17. Fried, I. (1982). Finite element computation of large rubber membrane deformations. Int. J. Num. Meth. Engr. 18:653–660.CrossRefMATHGoogle Scholar
  18. Gaetani, P., Tartara, F., Tancioni, F., Rodriguez y Baena, R., Casari, E., Alfano, M. and Grazioli, V. (1997). Deficiency of total collagen content and of deoxypyridinoline in intracranial aneurysm walls. FEBS Letters 404:303–306.CrossRefGoogle Scholar
  19. Gibbons, G.H. and Dzau, V.J. (1994). The emerging concept of vascular remodeling. Mech. of Disease 330:1431–1438.Google Scholar
  20. Green, A.E. and Zerna, W. (1954). Theoretical Elasticity. Oxford: Clarendon Press.MATHGoogle Scholar
  21. Green, A.E. and Adkins, J.E. (1970). Large Elastic Deformations. Oxford: Clarendon Press.MATHGoogle Scholar
  22. Hademenos, G.J., Massoud, T., Valentino, D.J., Duckwiler, G. and Vinuela, F. (1994). A nonlinear mathematical model for the development and rupture of intracranial saccular aneurysms. Neurol. Res. 16:376–384.Google Scholar
  23. Hegedus, K. (1984). Some observations on reticular fibers in the media of the major cerebral arteries. Surg. Neurol. 22:301–307.CrossRefGoogle Scholar
  24. 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. Int. J. Solids Structures 31:3375–3386.CrossRefMATHGoogle Scholar
  25. Hsu, F.P.K., Liu, A.M.C., Downs, J., Rigamonti, D. and Humphrey, J.D. (1995). A triplane video-based experimental system for studying axisym-metrically inflated biomembranes. IEEE Trans. Biomed. Engr. 42:442–450.CrossRefGoogle Scholar
  26. Humphrey, J.D., Strumpf, R.K. and Yin, F.C.P. (1992). A constitutive theory for biomembranes: Application to epicardium. ASME J. Biomech. Engr. 114:461–466.CrossRefGoogle Scholar
  27. Humphrey, J.D. (1995). Arterial wall mechanics: Review and directions. Crit. Rev. Biomed. Engr. 23:1–162.Google Scholar
  28. Humphrey, J.D. and Kyriacou, S.K. (1996). The use of Laplace’s equation in aneurysm mechanics. Neurol. Res. 18:204–208.Google Scholar
  29. Humphrey, J.D. (1998). Computer methods in membrane biomechanics. Comp. Meth. Biomech. Biomed. Engr. 1:171–210.CrossRefGoogle Scholar
  30. Humphrey, J.D. (2002) Cardiovascular Solid Mechanics: Cells, Tissues, and Organs. New York: Springer-Verlag.CrossRefGoogle Scholar
  31. Hung, E.J.N. and Botwin, M.R. (1975). Mechanics of rupture of cerebral saccular aneurysms. J. Biomech. 8:385–392.CrossRefGoogle Scholar
  32. Jain, K.K. (1963). Mechanism of rupture of intracranial saccular aneurysms. Surg. 347–350.Google Scholar
  33. Kosierkiewicz, T.M., Factor, S.M. and Dickson, D.W. (1994). Immunocytochemical studies of atherosclerotic lesions of cerebral berry aneurysms. J. Neuropath. Exp. Neurol. 53:399–406.CrossRefGoogle Scholar
  34. Kraus, H. (1967). Thin Elastic Shells. New York: Wiley.MATHGoogle Scholar
  35. Kyriacou, S.K. and Humphrey, J.D. (1996). Influence of size, shape and properties on the mechanics of axisymmetric saccular aneurysms. J. Biomech. 29:1015–1022. Erratum (1997). 30:761.CrossRefGoogle Scholar
  36. Kyriacou, S.K., Schwab, C. and Humphrey, J.D. (1996). Finite element analysis of nonlinear orthotropic hyperelastic membranes. Comp. Mech. 18:269–278.CrossRefMATHGoogle Scholar
  37. Kyriacou, S.K., Shah, A. and Humphrey, J.D. (1997). Inverse finite element characterization of nonlinear hyperelastic membranes. J. Appl. Mech. 64:257–262.CrossRefMATHGoogle Scholar
  38. Langille, B.L. (1993). Remodeling of developing and mature arteries: endothelium, smooth muscle, and matrix. J. Cardiovasc. Pharmacol. 21:S11–S17.CrossRefGoogle Scholar
  39. Libai, A. and Simmonds, J.G. (1988). The Nonlinear Theory of Elastic Shells. New York: Academic Press.MATHGoogle Scholar
  40. MacDonald, D.J., Finlay, H.M. and Canham, P.B. (2002). Directional wall strength in saccular brain aneurysms from polarized light microscopy. Ann. Biomed. Engr. (submitted)Google Scholar
  41. Milnor, W.R. (1989). Hemodynamics. Baltimore: Williams and Wilkens.Google Scholar
  42. Payne, A.R. (1974). Hysteresis in rubber vulcanizates. J. Polym. Sci. 48:169–195.CrossRefGoogle Scholar
  43. Pipkin, A.C. (1968). Integration of an equation in membrane theory. ZAMP 19:818–819.CrossRefMATHGoogle Scholar
  44. Ryan, J.M. and Humphrey, J.D. (1999). Finite element based predictions of preferred material symmetries in saccular aneurysms. Ann. Biomed. Engr. 27:641–647.CrossRefGoogle Scholar
  45. Scott, S., Ferguson, G.G., Roach, M.R. (1972). Comparison of the elastic properties of human intracranial arteries and aneurysms. Can. J. Physiol. Pharmacol. 50:328–332.CrossRefGoogle Scholar
  46. Sekhar, L.N., Heros, R.C. (1981). Origin, growth and rupture of saccular aneurysms: A review. Neurosurg. 8:248–260.CrossRefGoogle Scholar
  47. Sekhar, L.N., Sclabassi, R.P., Sun, M., Blue, H.B. and Wasserman, J.F. (1988). Intra-aneurysmal pressure measurements in experimental saccular aneurysms in dogs. Stroke 19:353–356.CrossRefGoogle Scholar
  48. Seshaiyer, P. and Humphrey, J.D. (2001). On the potentially protective role of contact constraints in saccular aneurysms. J. Biomech. 34:607–612.CrossRefGoogle Scholar
  49. Seshaiyer, P., Shah, A.D., Kyriacou, S.K. and Humphrey, J.D. (2001). Multiaxial mechanical behavior of human saccular aneurysms. Comp. Meth. Biomech. Biomed. Engr. 4:281–290.CrossRefGoogle Scholar
  50. Shah, A.D., Harris, J.L., Kyriacou, S.K. and Humphrey, J.D. (1997). Further roles of geometry and properties in saccular aneurysm mechanics. Comp. Meth. Biomech. Biomed. Engr. 1:109–121.CrossRefGoogle Scholar
  51. Shah, A.D. and Humphrey, J.D. (1999). Finite strain elastodynamics of saccular aneurysms. J. Biomech. 32:593–599.CrossRefGoogle Scholar
  52. Simkins, T.E. and Stehbens, W.E. (1973). Vibrational behavior of arterial aneurysms. Lett. Appl. Engr. Sci. 1:85–100.Google Scholar
  53. Stehbens, W.E. (1990). Pathology and pathogenesis of intracranial berry aneurysms. Neurol. Res. 12:29–34.Google Scholar
  54. Steiger, H.J., Aaslid, R., Keller, S. and Reulen, H.J. (1986). Strength, elasticity and viscoelastic properties of cerebral aneurysms. Heart Vessels 5:41–46.CrossRefGoogle Scholar
  55. Steiger, H.J. (1990). Pathophysiology of development and rupture of cerebral aneurysms. Acta Neurochir. Suppl. 48:1–57.Google Scholar
  56. Steigmann, D.J. (1990). Tension field theory. Proc. R. Soc. Lond. A 429:141–173.CrossRefMATHMathSciNetGoogle Scholar
  57. Toth, M., Nadasy, G.L., Nyary, I., Kerenyi, T., Orosz, M., Molnarka, G. and Monos, E. (1998). Sterically inhomogeneous viscoelastic behavior of human saccular cerebral aneuryms. J. Vasc. Res. 35:345–355.CrossRefGoogle Scholar
  58. White, J.C. and Sayre, G.P. (1961). Experimental destruction of the media for the production of intracranial arterial aneurysms. J. Neurosurg. 18:741–745.CrossRefGoogle Scholar
  59. Whittaker, P., Schwab, M.E. and Canham, P.B. (1988). The molecular organization of collagen in saccular aneurysms assessed by polarized light microscopy. Conn. Tiss. Res. 17:43–54.CrossRefGoogle Scholar
  60. Wiebers, D.O., Whisnant, J.P., Sundt, T.M. and O’Fallon, W.M. (1987). The significance of unruptured intracranial aneurysms. J. Neurosurg. 66:23–29.CrossRefGoogle Scholar
  61. Wiebers, D.O. et al. (1998) Unruptured intracranial aneurysms—risk of rupture and risks of surgical intervention. International study of unruptured intracranial aneurysms investigators. New Engl. J. Med. 339:1725–1733.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Wien 2003

Authors and Affiliations

  • J. D. Humphrey
    • 1
  1. 1.Biomedical EngineeringTexas A&M UniversityCollege StationUSA

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