On the Role of a Nonlinear Stress-Strain Relation in Brain Trauma

We investigate how a nonlinear stress-strain relation (that leads to a stiffening of the brain matter under strain) influences the brain dynamics in traumatic situations. We numerically simulate rapid rotational accelerations and decelerations of a human head using our generalization of the viscoelastic Kelvin-Voigt brain injury model that includes an experimentally established dependency of stress on strain. The rotational loads are expressed in terms of the Brain Injury Criterion, which we developed to extend the translational Head Injury Criterion to arbitrary head motions. Under traumatic loads corresponding to HIC15 =700, our model predicts that the brain stiffening reduces the maximal strain near the skull by up to 70%, but leads to a distribution of relatively high strain values throughout the brain. We show how the brain’s complex geometry enhances the random spatial distribution of high strain values.