Modal and temporal analysis of head mathematical models.

The basic hypotheses used during these investigations were based on the vibration analysis of the head, which demonstrated that the head is not a solid nondeformable body, but a complex structure including deformable elements. Laboratoire des Systemes Biomecanique (LSBM) has recently proposed three mathematical models: a lumped model, a finite element model of the head in its sagittal plane, and a three-dimensional finite element model. These models were validated by their modal behavior and enabled the lesion mechanisms to be distinguished as a function of the spectral characteristics of the shock. The objective of this study is to complete these modal results by temporal analysis of the models by calculating the evolution of the intracranian mechanical parameters under shock conditions. To describe the head's dynamic behavior in the temporal domain, constant energy shocks of variable duration were simulated to evaluate their influence on different quantities as the intracerebral stresses in terms of compression, tensile, and shearing stresses, the relative brain-skull displacement, and the skull deformation. The importance of modal behavior of the head is illustrated by analyzing its temporal response to variable duration impacts, thus exciting very different frequencies. For a triangular shock, the critical duration times are between 10 and 15 x 10(-3) s, which correspond to impacts that excite the first resonance frequency of the head. Taking modal behavior into consideration in developing the finite element model leads to a harmonization of the calculated intracerebral stresses, even for short duration shocks. So, when the head is considered as a complex structure made up of several deformable elements, risk limitation is conditioned by an impact energy reduction for frequencies close to the natural frequencies of the structure. In the time field, the objective will be to avoid a number of impact shapes and durations. Therefore, the aim will not be to dampen the impact at any cost, but to damper it in an "intelligent" manner. In the future, this will allow the reduction of an injury mechanism-related risk, without increasing the risk of an injury generated by another mechanism.