Mathematical model of a head subjected to an angular acceleration

Bycroft, G. N.<sup>1</sup>

Affiliations

¹Stanford Research Institute, Menlo Park, California 94025, U.S.A.†

Abstract and keywords

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 of 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 × 10³ rad/sec² is necessary to produce concussion in man.

Keywords:

Links

DOI: 10.1016/0021-9290(73)90007-9

PubMed: 4201261

WoS: A1973Q698200007

History

Received: 1972-11-01

Cited Works (3)

Year	Entry
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Cited By (18)

Year	Entry
2001	Zhang L, Yang KH, King AI. Biomechanics of neurotrauma. Neurol Res. March–April 2001;23(2-3):144-156.
1998	Lawson AR, Sadeghi MM. Finite element modelling of blunt or non-contact head injuries. In: Proceedings of the 16th International Technical Conference on the Enhanced Safety of Vehicles (ESV). May 31–June 4, 1998; Windsor, Ontario, Canada.2080-2092.
1991	Willinger R, Césari D, Kopp CM. Brain tolerance in the frequency field. In: Proceedings of the 13th International Technical Conference on Experimental Safety Vehicles (ESV). November 4-7, 1991; Paris, France.940-947.
1973	Ommaya AK, Thibault L. Head and spinal injury tolerance with no direct head impact. In: Proceedings of the 1973 International IRCOBI Conference on the Biomechanics of Impact. June 26-27, 1973; Amsterdam, The Netherlands.311-319.
1993	Thibault LE. Brain injury from the macro to the micro level and back again: what have we learned to date? In: Proceedings of the 1993 International IRCOBI Conference on the Biomechanics of Impact. September 8-10, 1993; Eindhoven, The Netherlands.3-25.
2009	Fijalkowski RJ, Yoganandan N, Zhang J, Pintar FA. A finite element model of region-specific response for mild diffuse brain injury. Stapp Car Crash J. 2009;53:193-213. SAE 2009-22-0007.
1975	Firoozbakhsh KK, DeSilva CN. A model of brain shear under impulsive torsional loads. J Biomech. 1975;8(1):65-73.
1975	Ljung C. A model for brain deformation due to rotation of the skull. J Biomech. 1975;8(5):263-274.
1976	King AI, Chou CC. Mathematical modelling, simulation and experimental testing of biomechanical system crash response. J Biomech. 1976;9(5):301-317.
1989	Margulies SS, Thibault LE. An analytical model of traumatic diffuse brain injury. J Biomech Eng. August 1989;111(3):241-249.
1995	Ueno K, Melvin JW. Finite element model study of head impact based on Hybrid III head acceleration: the effects of rotational and translational acceleration. J Biomech Eng. August 1995;117(3):319-328.
1997	Donnelly BR, Medige J. Shear properties of human brain tissue. J Biomech Eng. November 1997;119(4):423-232.
1982	Gennarelli TA, Thibault LE. Biomechanics of acute subdural hematoma. J Trauma. 1982;22(8):680-686.
1999	Huang H-M, Lee M-C, Chiu W-T, Chen C-T, Lee S-Y. Three-dimensional finite element analysis of subdural hematoma. J Trauma. September 1999;47(3):538-544.
2002	Ivarsson J. Physical Modeling of Brain and Head Kinematics [PhD thesis]. Göteburg, Sweden: Chalmers University of Technology; 2002.
1990	Lee E-S. A Large-Strain, Transient Dynamic Analysis of Head Injury Problems by the Finite Element Method [PhD thesis]. Atlanta, GA: Georgia Institute of Technology; October 1990.
1987	Margulies SS. Biomechanics of Traumatic Coma in the Primate [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 1987.
2001	Zhang L. Computational Biomechanics of Traumatic Brain Injury: An Investigation of Head Impact Response and American Football Head Injury [PhD thesis]. Detroit, MI: Wayne State University; May 2001.