A Mathematical Model for the Behavior of the Brain When the Human Head Is Subjected to Impulsive Loads

The subject matter of this paper is concerned with the theoretical determination of the behavior of the brain when the human head is subjected to external impulsive loads. The mathematical analysis is made for the axisymmetric response of an inviscid compressible fluid loaded impulsively by its elastic spherical shell container. In the analysis first the solution for an initial value problem is obtained; later the transient response of the fluid for an arbitrary velocity input of the shell is constructed by means of convolution integral. For the numerical results, a characteristic time is defined and the excess pressure distribution in the fluid is evaluated for various deceleration times comparable with this characteristic time. Presented at the Symposium on Biodynamics Models and Their Applications held at Dayton, Ohio, on 26-28 Oct 1970. Sponsored in part by Public Health Service, Washington, D. C. Paper also included in AD0739501.