A mathematical model for the determination of viscoelastic behavior of brain in vivo--I Oscillatory 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 dilation, which is considered known from other sources. Part I of this study considers steady oscillations of the probe. A transcendental equation for the complex shear modulus is established in terms of probe displacement and force amplitude ratio and phase lag and is solved for specific test data. The corresponding stress and displacement fields are evaluated so that the probe influence may be assessed.