A study of rotational brain injury

Abstract

Of concern in the paper is an investigation on brain injuries which may occur owing to an input angular acceleration of the head. The study is based on the use of an improved mathematical model for the cranium. The eccentricity of the braincase is incorporated through the consideration of a prolate spheroidal shell as the representative of the skull. Also the dissipative mechanical behaviour of the brain material (as per the observations of experimenters) has been accounted for by considering the material contained in the shell as viscoelastic. The problem is formulated in terms of prolate spheroidal coordinates. The singularities of the governing equations of motion (when expressed in the prolate coordinate system) are removed by a suitable transformation of the concerned dependent variable, viz. the one that stands for the angular displacement of a representative point of the system. In the first place the solution of the boundary value problem is sought in the Laplace transform space, by employing a finite difference technique. Use of the alternating-direction-implicit method together with Thomas algorithm was made for obtaining the angular acceleration in the transformed space. The Laplace inversion is also carried out with the help of numerical procedures (Gauss quadrature formula is used for this purpose). The results of the parametric study are presented through graphs. The plots illustrate the shear stresses and strains in the brain medium. A meaningful comparison of the computational results with those of previous investigations indicate that the eccentricity of the braincase plays a significant role in causing injury to the brain.