[en] In recent years, the mechanical study of the brain has become a major topic in the field of biomechanics. A global biomechanical model of the brain could find applications in neurosurgery and haptic device design. It would also be useful for car makers, who could then evaluate the possible trauma due to impact. Such a model requires the design of suitable constitutive laws for the different tissues that compose the brain (i.e. for white and for gray matters, among others).
Numerous constitutive equations have already been proposed, based on linear elasticity, hyperelasticity, viscoelasticity and poroelasticity. Regarding the strong strain-rate dependence of the brain’s mechanical behaviour, we decided to describe the brain as a viscoelastic medium. The design of the constitutive law was based on the Caputo fractional derivation operator. By definition, it is a suitable tool for modeling hereditary materials. Indeed, unlike integer order derivatives, fractional (or real order) operators are non-local, which means they take the whole history of the function into account when computing the derivative at current time t.
The model was calibrated using experimental data on simple compression tests performed by Miller and Chinzei. A simulated annealing algorithm was used to ensure that the global optimum was found. The fractional calculus-based model shows a significant improvement compared to existing models. This model fits the experimental curves almost perfectly for natural strains up to − 0.3 and for strain-rates from 0.64s − 1 to 0.64 10− 2 s − 1.
Disciplines :
Materials science & engineering
Author, co-author :
Libertiaux, Vincent ; Université de Liège - ULiège > Département Argenco : Secteur MS2F > Mécanique des solides
Pascon, Frédéric ; Université de Liège - ULiège > Département ArGEnCo > Département ArGEnCo
Language :
English
Title :
Viscoelastic Modeling of Brain Tissue: A Fractional Calculus-Based Approach
Publication date :
2009
Event name :
11th EUROMECH-MECAMAT Conference
Event organizer :
Professor Jean-François Ganghoffer Professor Franco Pastrone
Event place :
Torino, Italy
Event date :
March 10-14, 2008.
Audience :
International
Main work title :
Mechanics of Microstructured Solids Cellular Materials, Fibre Reinforced Solids and Soft Tissues
Editor :
Ganghoffer, Jean-François
Pastrone, Franco
Publisher :
Springer, Berlin, Germany
ISBN/EAN :
978-3-642-00910-5
Collection name :
Lecture Notes in Applied and Computational Mechanics: 46
Adolfsson, K.: Models and numerical proecures for fractional order viscoelasticity. PhD thesis, Chalmers university of Technology (2003)
Adolfsson, K., Enelund, M.: Fractional derivative viscoelasticity at large deformations. Nonlinear dynamics 33, 301-321 (2003)
Brands, D., Peters, G., Bovendeed, P.: Design and numerical implementation of a 3d non-linear viscoelastic constitutive model for brain tissue during impact. Journal of Biomechanics 37, 127-134 (2004)
Carpinteri, A., Mainardi, F.: Fractals and fractional calculus in continuum mechanics. Springer, Heidelberg (2006)
Clatz, O.: Analysis and prediction of the brain deformation during a neurosurgical procedure. Master's thesis, ENS Cachan (2002)
Darvish, K., Crandall, J.: Nonlinear viscoelastic effects in oscillatory shear deformation of brain tissue. Medical Engineering & Physics 23, 633-645 (2001)
Diethelm, K., Ford, N.J., Freed, A.D.: A predictor-corrector approach for the numerical solution of fractional differential equations. Non linear dynamics 29, 3-22 (2002)
Diethelm, K., Freed, A.D.: 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, 203-215 (2006)
Ford, N.J., Simpson, A.C.: The numerical solution of fractional di erential equations: speed versus accuracy. Technical report, Manchester Center for Computational Mathematics (2001)
Hault, A., Drazetic, P., Razafimahery, F.: 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)
Miga, M., Paulsen, K., Hoopes, P., Kennedy, F., Hartov, A., Roberts, D.: In vivo modelling of interstitial pressure in the brain under surgical load using finite elements. Journal of Biomechanical Engineering 122, 354-363 (2000)
Miga, M., Paulsen, K., Hoopes, P., Kennedy, F., Hartov, A., Roberts, D.: In vivo quantification of a homogeneous brain deformation model for updating preoperative images during surgery. IEEE Transactions on Biomedical Engineering 47, 266-273 (2000)
Miller, K.: Constitutive model of bain tissue suitable for finite element analysis of surgical procedures. Journal of Biomechanics 32, 531-537 (1999)
Miller, K., Chinzei, K.: Constitutive modelling of brain tissue: experiment and theory. Journal of Biomechanics 30, 1115-1121 (1997)
Miller, K., Chinzei, K.: Mechanical properties of brain tissue in tension. Journal of Biomechanics 35, 483-490 (2002)
Podlubny, I.: Fractional differential equations. London Academic Press, London (1999)
Sarron, J.C., Blondeau, C., Guillaume, A., Osmont, D.: Identification of linear viscoelastic constitutive models. Journal of Biomechanics 33, 685-693 (2000)
Skrinjar, O., Nabavi, A., Duncan, J.: Model-driven brain shift compensation. Medical Image Analysis 6, 361-373 (2002)
Velardi, F., Fraternali, F., Angelillo, M.: Anisotropic constitutive equations and experimental tensile behavior of brain tissue. Biomech. Model Mechanbiol. 5(53), 61 (2006)
Wittek, A., Miller, K., Kikinis, R., Warfield, S.: Patient-specific model of brain deformation: application to medical image registration. Journal of Biomechanics 40, 919-929 (2007)