Medical Engineering & Physics
Volume 28, Issue 5 , Pages 455-459 , June 2006

The constitutive properties of the brain paraenchyma: Part 2. Fractional derivative approach

Received 19 July 2004 ,Revised 10 January 2005 ,Accepted 15 July 2005.

References 

  1. Fung YC. Biomechanics: mechanical properties of living tissues. New York: Springer; 1981;
  2. Brett PN, Fraser CA, Henningan M, Griffiths MV, Kamel Y. Automatic surgical tools for penetrating flexible tissues. IEEE Eng Med Biol. 1995;264–270
  3. Burdea G. Force and touch feedback for virtual reality. New York: Wiley; 1996;
  4. Pamidi MR, Advani SH. Nonlinear constitutive relation for human brain tissue. ASME J Biomech Eng. 1978;100:44–48
  5. Mendis KK, Stalnaker RL, Advani SH. A constitutive relationship for large deformation finite element modeling of brain tissue. ASME J Biomech Eng. 1995;117:279–285
  6. Miller K, Chinzei K. Constitutive modelling of brain tissue: Experiment and theory. J Biomech. 1997;30:1115–1121
  7. Miller K, Chinzei K. Mechanical properties of brain tissue in tension. J Biomech. 2002;35:483–490
  8. Kohandel M, Sivaloganathan S, Tenti G, Drake JM. The constitutive properties of brain parenchyma Part 1. Strain energy approach. Med Eng Phys 2006;28:449–54.
  9. Hakim S. Biomechanics of hydrocephalus. Acta Neorologica Latinoamericana. 1971;17:169–174
  10. Nagashima T, Tamaki N, Matsumoto S, Horwitz B, Seguchi Y. Biomechanics of hydrocephalus: a new theoretical model. Neurosurgery. 1987;21:898–904
  11. Kaczmarek M, Subramaniam RP, Neff SR. The hydromechanics of hydrocephalus: steady-state solution for cylindrical geometry. Bulletin of Mathematical Biology. 1997;59:295–323
  12. Tenti G, Sivalagonathan S, Drake JM. Brain biomechanics: steady-state consolidation theory of hydrocephalus. Canadian Applied Math Quarterly. 1999;7:93–110
  13. Estes MS, McElhaney JH. Response of brain tissue of compressive loading. ASME Paper No. 70-BHF-13; 1970.
  14. Galford JE, McElhaney JH. A viscoelastic study of scalp, brain and dura. J Biomech. 1970;3:211–221
  15. Podlubny I. Fractional differential equations. Academic Press; 1999;
  16. Bagley RL, Torvik PJ. Fractional calculus—a different approach to the analysis of viscoelastically damped structures. AIAA J. 1983;25(5):741
  17. Schiessel H, Metsler R, Blumen A, Nonnenmacher T. Generalized viscoelastic models: their fractional equations with solutions. J Phys A. 1995;28:6567
  18. Bagley RL, Torvik PJ. A theoretical basis for the application of fractional calculus to viscoelasticity. J Rheol. 1983;27(3):201
  19. Findley WN, Lai JS, Onaran K. Creep and relaxation of nonlinear viscoelastic materials. Dover; 1976;
  20. Zener C. Elasticity and anelasticity of metals. Chicago University Press; 1948;
  21. Scott-Blair GW. The role of psychophysics in rheology. J Colloid Sci. 1947;2:21

PII: S1350-4533(05)00185-2

doi: 10.1016/j.medengphy.2005.07.023

Medical Engineering & Physics
Volume 28, Issue 5 , Pages 455-459 , June 2006