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Mathematical models of head injuries.
NIOSH 1973 Jul; :1-61
The effect of rotational and translational acceleration on the brain was studied using two different mathematical analyses. A mathematical model of a head subjected to an angular acceleration was developed in which the brain was treated as a viscoelastic medium to study the effect of rotational acceleration. A rapid decrease in shear strain was noted in this model from the outside to the center of the brain. Correlating this model with experimental work using monkeys demonstrated that a shear strain greater than cause a concussion. From that finding it was concluded that an angular acceleration greater than 3500 radians/second squared is needed to cause a concussion in man. A computer program was created to determine the stresses in a mathematical model of the skull and brain subjected to a direct blow causing translation of the head without rotation for the translational acceleration study. The brain was treated as a simple compressible fluid or as a viscoelastic medium with the measured properties of brain matter. Cavitation appeared in wedge shaped areas similar to those of lesions observed clinically. No difference was noted between the results for a brain treated as viscoelastic fluid and for a brain treated as a simple compressible fluid. The authors conclude that brain damage results from large shear or tensile strains which are produced by both angular acceleration of the head and by direct blows causing translation of the head.
NIOSH-Grant; Head-injuries; Accident-analysis; Laboratory-animals; Brain-damage; Brain-edema; Mathematical-models; Neurology; Mathematics; Injuries; Viscoelasticity; Tensility; Methodology
Applied Mathematics, Stanford Research Institute, 333 Ravenswood Ave., Menlo Park, California 94025
Final Grant Report
NTIS Accession No.
Stanford Research Institute, Menlo Park, California, NIOSH Grant No. R01-OH-00343, 64 pages, 47 references
Stanford Research Institute, Menlo Park, California
Page last reviewed: September 2, 2020
Content source: National Institute for Occupational Safety and Health Education and Information Division