Package Cushioning for the Human Head—1: Analytical Considerations

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Abstract
The 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 spring-dashpot simulate the composite elastic and dissipative properties of the helmet, hair, skin, skull, and the real wall. The exact closed-form wave-propagation solution was obtained by exploiting the hyperbolic nature of the Laplace transformed equations. The infinite series solution suitable for all values of time was also obtained via the residue theorem. The system response was found to be dependent on 4 dimensionless ratios: 1. The brain to skull mass. 2. The skull to closed brain stiffness. 3. The damping factor of the skull. 4. The impact velocity to the brain wave speed. Results were presented for a range of parameter values realistic to the head injury problem. The severity of the impact was evaluated by the ratio between the cavitation duration at contrecoup and the contact duration between the head and the wall.

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