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A viscoelastic fluid model for brain injuries
Author(s) -
Cotter C. S.,
Smolarkiewicz P. K.,
Szczyrba I. N.
Publication year - 2002
Publication title -
international journal for numerical methods in fluids
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.938
H-Index - 112
eISSN - 1097-0363
pISSN - 0271-2091
DOI - 10.1002/fld.287
Subject(s) - viscoelasticity , classical mechanics , mechanics , physics , newtonian fluid , elasticity (physics) , turbulence , linear elasticity , finite element method , thermodynamics
Due to its elasticity, the human brain material can support shear (equivoluminal) waves. Earlier attempts to explain certain brain injuries via arguments of the classical theory of viscoelasticity exploited the Voigt model—a linear system of differential equations where the motion of the brain tissue depends merely on the balance between viscous and elastic forces. Although Voigt model solutions illustrate the role of the viscoelastic mechanics in brain injuries, they have limited use for modelling realistic cases which, for example, evince strongly localized displacements of the brain tissue. We have extended the Voigt model to a non‐linear viscoelastic fluid model, thereby dispensing with simplifying assumptions of vanishing advective transport. The resulting non‐Newtonian fluid model admits non‐linear phenomena such as steepening of the wave fronts as well as wave overturning and their subsequent turbulent breaking. The posed equations are solved numerically, and the solution procedure are validated against small‐perturbation linear theory and closed‐form Voigt‐model solutions available in the literature. Our non‐linear numerical results suggest existence of a ‘brain turbulence’ phenomenon. They are in qualitative agreement with the results of medical research, especially, with regard to the diffuse axonal injuries which are observed to occur in a highly localized manner near the border between the gray and the white matter. Copyright © 2002 John Wiley & Sons, Ltd.