MATHEMATICAL-MODEL OF A HEAD SUBJECTED TO AN ANGULAR ACCELERATION

The brain is modelled as a spherical viscoelastic medium attached to the inside of a rigid spherical shell. The mechanical wave motion which is generated in the brain when the head is subjected to an angular acceleration of a particular amplitude and duration is calculated and the results are compared with experimental data on monkeys. The experimental data show that the threshold of angular acceleration necessary to cause concussion varies with the duration of the acceleration in a manner predicted approximately by the model. The ″two-thirds power scaling law″ is directly established for an elastic model but is shown to be deficient for a viscoelastic model fo the brain. A value of shear strain of 0. 05 in the region of the upper reticular formation is deduced as that necessary to cause concussion. The model predicts that an angular acceleration greater than 3. 5 multiplied by 10**3 rad/sec**2 is necessary to produce concussion in man.