A mathematical model for the determination of viscoelastic behavior of brain in vivo--II relaxation response

Abstract

In a recent experiment for determining the mechanical response of brain in vivo. a probe, inserted through scalp, skull and dura, is placed in contact with and normal to the brain, given a prescribed motion, and the time variation of corresponding force is measured. In the corresponding continuum mechanical model, brain is idealized as a linear isotropic viscoelastic solid constrained by a rigid skull. At the mating surface, the shear stress and normal displacement vanish everywhere except under the probe which exerts a local radial displacement. This model introduces effective viscoelastic moduli in shear, which is unknown, and in dilatation, which is considered known from other sources. Part II of this study is concerned with stress relaxation induced by a small step displacement of the probe. From the solution of the corresponding quasi-static boundary value problem, a nonlinear Volterra integral equation is established from which the shear stress relaxation function can be solved in terms of measured probe displacement and force. A numerical method of solution is developed.