Optimal Protection in Direct Closed Head Impact

The direct closed head impact problem was idealized as a fluid-filled cylinder attached to a spring-dashpot element striking a rigid wall. The rigid cylinder represents the skull, the fluid denotes the brain and the cerebrospinal fluid (CSF) and the lumped spring-dashpot element simulates the composite elastic and dissipative properties of the helmet, hair, skin, skull and the real wall. This paper concerns the inverse problem, i.e., what material and inertial properties should the helmet or padding have to afford optimal protection in a direct closed head impact? The answer was found in terms of 4 dimensionless ratios: (1) the brain to skull mass, (2) the skull to closed brain stiffness, (3) the damping factor of the skull, and (4) the impact speed of the cylinder to the brain wave speed. The solution to the problem was achieved through hybrid computation using as the Index of Performance the time averaged pressure at contrecoup beyond the cavitation pressure of the fluid. Given a set of impact and system parameters, the optimal choice consists of making the value of the stiffness ratio as small as possible and still completely compressing the spring. Then, for a given mass ratio, the optimum damping ratio is found from a simple graph.