Biomechanics of the brain: A theoretical and numerical study of Biot's equations of consolidation theory with deformation-dependent permeability

International Journal of Non-Linear Mechanics

Volumn 40, Issue 9, 2005, Pages 1149-1159

  Sivaloganathan, S ^a   Stastna, M ^a   Tenti, G ^a   Drake, J M ^b  

^a UNIVERSITY OF WATERLOO   (Canada)

^b HOSPITAL FOR SICK CHILDREN   (Canada)

Author keywords

Consolidation theory; Semigroups; Variable permeability

Indexed keywords

BRAIN; COMPUTATIONAL GEOMETRY; DEFORMATION; MATHEMATICAL MODELS; MECHANICAL PERMEABILITY; PROBLEM SOLVING;

BIOT'S THEORY; BRAIN ABNORMALITIES; CONSOLIDATION THEORY; HYDROCEPHALUS; SEMIGROUPS; VARIABLE PERMEABILITY;

BIOMECHANICS;

EID: 25644439327     PISSN: 00207462     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijnonlinmec.2005.04.004     Document Type: Article

References (15)

1. M. Kaczmarek, R.P Subramanian, and S.R. Neff The hydromechanics of hydrocephalus: steady-state solutions for cylindrical geometry Bull. Math. Biol. 59 1997 295 323
2. M. Stastna, G. Tenti, S. Sivaloganathan, and J.M. Drake Brain biomechanics: consolidation theory of hydrocephalus. Variable permeability and transient effects CAMQ 7 1 1999 111 124
3. M. Stastna, S. Sivaloganathan, G. Tenti, and J.M. Drake Brain biomechanics: an exact solution and asymptotics of slow variations, for the time dependent equations of consolidation theory Dynam. Continuous Discrete Impulsive Syst. 5 1999 415 425
4. M.A. Biot General theory of three-dimensional consolidation J. Appl. Phys. 12 1941 155 164
5. J. Bear Dynamics of Fluids in Porous Media 1988 Dover Publications New York
6. R.L. Schiffman Theories of Consolidation 2000 University of Colorado Press
7. H.F. Wang Theory of Linear Poroelasticity with Applications to Geomechanics and Hydrogeology 2000 Princeton University Press Princeton
8. World Scientific Publishing (Ed.), Mathematical Modelling of Flow through Porous Media, World Scientific Publishing, Singapore, 1995.
9. G. Tenti, S. Sivaloganathan, and J.M. Drake Brain biomechanics: steady state consolidation theory of hydrocephalus CAMQ 7 1 1999 93 110
10. S. Sivaloganathan, G. Tenti, and J.M. Drake Mathematical pressure volume models of the cerebrospinal fluid Appl. Math. Comput. 94 1998 243 266
11. V.C. Mow, M.K. Kwan, W.M. Lai, and M.H. Holmes A finite deformation theory for nonlinearly permeable soft hydrated biological tissues g.W. Schmid-Schonbein L.L.-Y. Woo B.w. Zweifich Frontiers in Biomechanics 1986 Springer New York
12. W.H. Press, S.A. Teukolsky, W.T. Veterling, and B.P. Flannery Numerical Recipes in C 1992 Cambridge University Press Cambridge
13. M.N. Ozisik Boundary Value Problems of Heat Conduction 1968 Dover NY
14. J.W. Jerome, Approximation of nonlinear evolution systems, in: Mathematics in Science & Engineering, vol. 164, Academic Press, New York, 1983.
15. S. Sivaloganathan, M. Stastna, G. Tenti, and J.M. Drake A Viscoelastic Model of the Brain Parenchyma with Pulsatile Ventricular Pressure Appl. Math. Comput. 165 2005 687 698