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Mathematical Model for Closed Head Impact
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Abstract
In order to understand better the head injury mechanism and to clarify the unsettled question as to whether the shear strain or the reduced pressure is the primary injury etiology during a given impact, a realistic model capable of predicting both the shear strain and the reduced pressure effects should be devised. The approach to such a realistic but complicated boundary value problem in biomechanics is achieved through the application of the finite element method. By use of the finite element displacement formulation, the human head is modeled as a viscoelastic core bonded to a thin viscoelastic shell, which simulates the brain and the skull, respectively.
For purpose of comparison, two configurations-a spherical shape and a prolate ellipsoid-have been used to describe the geometry of the human head. By applying an impact load over a small area of the shell, the head injury mechanisms-such as cavitation, caused by excessive tensile stress, and rotation, produced by large shear strain-along with their possible damage locations, are simulated. Linear viscoelastic properties are assumed for both the core material and the shell. The equations of motion for the problem are in the form of second-order matrix differential equations. Solutions are obtained through the matrix iterative method.
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Chan, H., "Mathematical Model for Closed Head Impact," SAE Technical Paper 741191, 1974, https://doi.org/10.4271/741191.Also In
References
- Poleck D. G. “The Body-What Happens to It in a Crash.” Traffic Safety 1967
- Gross A. G. “A New Theory on the Dynamics of Brain Concussion and Brain Injury.” Jrl. Neurosurg 15 1958
- Gurdjian E. S. Webster J. E. Lissner H. R. “Observations on the Mechanisms of Brain Concussion, Contusion, and Laceration.” Surgery, Gynec. & Obst 101 1955
- Sellier K. Unterharnscheidt F. “Mechanik der Swealteinwirkung auf den Schädel.” Excerpta Med. International Congress Series 93 1965
- Lindgren S. O. “Experimental Studies of Mechanical Effects in Head Injury.” Acta Chirurgica Scandinavica, Supp. 360 1966
- Holbourn A. H. S. “Mechanics of Head Injury.” Lancet 2 1943
- Ommaya A. K. Hirsch A. E. Martinez J. “The Role of Whiplash in Cerebral Concussion.” Paper 660804 Proceedings of Tenth Stapp Car Crash Conference 10 New York: Society of Automotive Engineers, Inc. 1966
- Hodgson H. S. Gurdjian E. S. Thomas L. N. “Experimental Skull Deformation and Brain Displacement Demonstrated by Flash X-Ray Technique.” Jrl. Neurosurg 25 1961
- Unterharnscheidt F. Higgins L. S. “Pathomorphology of Experimental Head Injury Due to Rotational Acceleration.” Acta Neuropathologica 12 1969
- Goldsmith W. “Biomechanics of Head Injury.” Proceedings of Symposium on Foundation and Objectives of Biomechanics San Diego, Englewood Cliffs, N.J. PrenticeHall 1970
- Liu W. K. “The Biomechanics of Spinal and Head Impact: Problems of Mathematical Simulation,” Proc. Symp. Biodynamic Modeling and Its Applications Dayton 1970
- Chan H. S. Liu Y. K. “The Asymmetric Response of a Fluid-Filled Spherical Shell?A Mathematical Simulation of a Glancing Blow to the Head.” Jrl. Biomechanics 7 1974
- Goldsmith W. “The Physical Processes Producing Head Injury.” Proceedings of Head Injury Conference Philadelphia: Lippincott 1966
- Anzelius A. “The Effect of an Impact on a Spherical Liquid Mass.” Acta. Path. Microbiol. Scand., Suppl. 48 1943
- Guttinger W. “Der Stosseffect auf eine Flassigkeitskugel als Grundlage einer Physikalischen Theoülie der Entstehung von Gehirnverletzungen.” Zeig. f. Naturforschung 5 1950
- Engin A. E. Liu Y. K. “Axisymmetric Responses of a Fluid-Filled Sperical Shell in Free Vibrations,” Jrl. Biomechanics 3 1 1970
- Engin A. E. “Axisymmetric Response of a FluidFilled Spherical Shell to a Local Radial Impulse-A Model for Head Injury.” Jrl. Biomechanics 2 3 1969
- Liu Y. K. Chan H. S. Nelson J. A. III “Intracranial Pressure Wave Propagation in Head Impact.” Proceedings Summer Computer Simulation Conference Boston 1971
- Hickling R. Wenner M. L. “Mathematical Model of a Head Subjected to an Axisymmetric Impact.” General Motors Research Laboratories Publication GMR-1242 Warren, Mich. August 2 1972
- Kenner V. H. Goldsmith W. “Dynamic Loading of a Fluid-Filled Spherical Shell.” Int. Jrl. Mech. Sci 14 1972
- Benedict J. V. Harris E. H. Rosenberg V. D. von “An Analytical Investigation of the Cavitation Hypothesis of Brain Damage.” Jrl. Basic Eng 92 3 1970
- Engin A. E. Roberts V. L. “A Mathematical Model for the Behavior of the Brain When the Human Head is Subjected to Impulsive Load.” Proceedings Biodynamic Modeling and its Application Dayton 1970
- Liu Y. Chandran K. B. “The Exact Solution to the Rotational Acceleration of Rigid Spherical Shells Filled with a Brain-Like Elastic Material,” Proceedings 10th Annual Meeting, Society of Engineering Science Raleigh November 1973
- Liu Y.King Chandran K. B. “The Exact Solution to the Translational Acceleration of Inviscid Compressible Fluid in Rigid Spherical Shells.” Math. Biosci., in press
- Liu Y.King Rosenberg D. U. von “A One-Dimensional Continuum Model of Direct Closed Head Impact.” Conference International Research Comm. on Biokinetics of Impacts Amsterdam 1973
- Liu Y.King Chandran K. B. “Package Cushioning for the Human Head.” ASME Annual Meeting New York November 1974
- Hayashi T. “Study of Intracranial Pressure Caused by Head Impact.” Jrl. Fac. of Eng., University of Tokyo 30 59 1969
- Davids N. Ray G. “Finite Element Analysis Methods in Dynamics of Pulsatile Flow.” Report on PHS Grant No. IR-01-HE-1 1289-03 National Heart Institute August 1969
- Oestreicher H. L. “Field and Impedance of an Oscillating Sphere in a Viscoelastic Medium with an Application to Biophysics.” Jrl. Acoust. Soc. Am 23 6 1951
- Wilson E. L. “Elastic Dynamic Response of Axisymmetric Structures.” Report No. 69-2, Structural Engineering Laboratory, University of California Berkeley 1969
- D'Ewart B. B. Jr. Farrell R. F. “The Computation of Dynamic Response Time Histories of a System Using a Matrix Iterative Technique.” Proceedings Matrix Method in Structural Mechanics Dayton 1966
- Koeneman J. B. “Viscoelastic Properties of Brain Tissue.” Masters Thesis, Case Institute of Technology 1966
- McElhaney J. H. Melvin J. W. Roberts V. L. “Dynamic Characteristic of the Tissue of the Head” Proceedings of Biomedical Engineering Conference Glasglow 1972
- Estes M. S. “Response of Brain Tissue to Compressive Loading.” ASME Paper 70-BHF-17 1970
- Fallenstein G. T. Hulee V. D. Melvin J. W. “Dynamic Mechanical Properties of Human Brain Tissues.” Jrl. Biomechanics 2 3 1969
- Engin A. E. Wang H. C. “A Mathematical Model to Determine Viscoelastic Behavior of In Vivo Primate Brain.” Jrl. Biomechanics 1970