Differential versus integral formulation of fractional hyperviscoelastic constitutive laws for brain tissue modelling

Journal of Computational and Applied Mathematics

Volumn 234, Issue 7, 2010, Pages 2029-2035

  Libertiaux, V ^a   Pascon, F ^a  

^a UNIVERSITY OF LIÈGE   (Belgium)

Author keywords

Brain tissue modelling; Fractional derivative; MittagLeffler's functions; Viscoelasticity

Indexed keywords

BIOLOGICAL TISSUES; BRAIN TISSUE; CAR MANUFACTURING; CONSTITUTIVE LAW; DERIVATION OPERATORS; FRACTIONAL DERIVATIVE; FRACTIONAL DERIVATIVES; GLOBAL MODELS; HAPTIC DEVICES; INTEGRAL FORMULATIONS; MECHANICAL STUDY; MITTAG-LEFFLER FUNCTIONS; MITTAGLEFFLER'S FUNCTIONS; STRAIN RATE DEPENDENCE; VISCOELASTIC MEDIUM;

AUTOMOBILE MANUFACTURE; BIOMECHANICS; BRAIN; BRAIN MODELS; ELASTICITY; NEUROSURGERY; STRAIN RATE; VISCOELASTICITY; VISCOSITY;

TISSUE;

EID: 77955305904     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2009.08.060     Document Type: Conference Paper

References (25)

1. O. Clatz, Analysis and prediction of the brain deformation during a neurosurgical procedure, Master Thesis, ENS Cachan, 2002
2. A. Hault, P. Drazetic, F. Razafimahery, Etudes des phenomenes d'interaction fluide/structure lors d'un choc a l'interieur de la boite cranienne, in: 17eme Congres Francais de Mecanique, 2005
3. O. Skrinjar, A. Nabavi, and J. Duncan Model-driven brain shift compensation Medical Image Analysis 6 2002 361 373
4. M. Miga, K. Paulsen, P. Hoopes, F. Kennedy, A. Hartov, and D. Roberts In vivo modelling of interstitial pressure in the brain under surgical load using finite elements Journal of Biomechanical Engineering 122 2000 354 363
5. M. Miga, K. Paulsen, P. Hoopes, F. Kennedy, A. Hartov, and D. Roberts In vivo quantification of a homogeneous brain deformation model for updating preoperative images during surgery IEEE Transactions on Biomedical Engineering 47 2000 266 273
6. J. Sarron, C. Blondeau, A. Guillaume, and D. Osmont Identification of linear viscoelastic constitutive models Journal of Biomechanics 33 2000 685 693
7. D. Brands, G. Peters, and P. Bovendeed Design and numerical implementation of a 3D non-linear viscoelastic constitutive model for brain tissue during impact Journal of Biomechanics 37 2004 127 134
8. K. Darvish, and J. Crandall Nonlinear viscoelastic effects in oscillatory shear deformation of brain tissue Medical Engineering and Physics 23 2001 633 645
9. F. Velardi, F. Fraternali, and M. Angelillo Anisotropic constitutive equations and experimental tensile behavior of brain tissue Biomechanics and Modeling in Mechanbiology 5 2006 53 61
10. K. Miller Constitutive model of brain tissue suitable for finite element analysis of surgical procedures Journal of Biomechanics 32 1999 531 537
11. K. Miller, and K. Chinzei Mechanical properties of brain tissue in tension Journal of Biomechanics 35 2002 483 490
12. A. Wittek, K. Miller, R. Kikinis, and S. Warfield Patient-specific model of brain deformation: Application to medical image registration Journal of Biomechanics 40 2007 919 929
13. P. Nutting A new general law of deformation Journal of the Franklin Institute 191 1921 679 685
14. A. Gemant On fractional differentials Philosophical Magazine 25 1938 540 549
15. I. Podlubny W. Ames, Fractional Differential Equations 1999 London Academic Press
16. K. Adolfsson, Models and numerical procedures for fractional order viscoelasticity, Chalmers University of Technology, 2003
17. K. Adolfsson, and M. Enelund Fractional derivative viscoelasticity at large deformations Nonlinear Dynamics 33 2003 301 321
18. K. Diethelm, and A. Freed Fractional calculus in biomechanics: A 3D viscoelastic model using regularized fractional-derivative kernels with application to the human calcaneal fat pad Biomechanics and Modeling in Mechanobiology 5 2006 203 215
19. A. Schmidt, L. Gaul, Application of fractional calculus to viscoelastically damped structures in the finite element method, in: Proceedings of the International Conference on Structural Dynamics Modelling, 2002, pp. 297306
20. M. Enelund, and G. Lesieutre Time domain modeling of damping using anelastic displacement fields and fractional calculus International Journal of Solids and Structures 36 1999 4447 4472
21. N. Ford, A. Simpson, The numerical solution of fractional differential equations: Speed versus accuracy, Internal Report, Manchester Center of Computational Mathematics, 2001
22. K. Diethelm, and A. Freed An efficient algorithm for the evaluation of convolution integrals Computers and Mathematics with Applications 51 2006 51 72
23. W. Deng Short memory principle and a predictorcorrector approach for fractional differential equations Journal of Computational and Applied Mathematics 206 2007 174 178
24. F. Mainardi, and A. Carpinteri Fractals and Fractional Calculus in Continuum Mechanics 2006 Springer
25. K. Diethelm, N. Ford, and A. Freed A predictorcorrector approach for the numerical solution of fractional differential equations Nonlinear Dynamics 29 2002 3 22 (Pubitemid 34945390)