This paper is part of our systematic effort to investigate the phenomena of traumatic head injury. It deals with a fluid-filled rigid container, moving with an initial velocity, striking a rigid wall through a spring and dashpot in parallel, so that an impulsive load is applied to the ensemble. This particular abstraction of the direct head impact phenomena appears to be ideal as a bridge between the simplistic one degree-of-freedom and the complex two- or three-dimensional continuum models of the same.

An exact closed-form (wave propagation) small-time solution for the linear problem associated with the above model was obtained and reported elsewhere. Using the exact solution to the posed problem as a basis, a computeraided finite-difference numerical solution was obtained for the system. The field descriptions of the fluid pressure and container acceleration depended on a small number of dimensionless parameters. These are :​ (1) The ratio of the velocity of the skull container (just prior to impact) to the wave speed in the cerebrospinal fluid and brain;​ (2) the brain to skull mass ratio;​ (3) the damping factor of the skull materials and (4) the brain to skull stiffness ratios. The head injury potential of a given impact is assessed as a function of the system response. jury potential.