A mathematical model of spinal response to impact

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Orne, David¹; Liu, Y. King²

A mathematical model of spinal response to impact

J Biomech. 1971;4(1):49-71

Affiliations

¹Department of Mechanical Engineering Sciences, Wayne State University, Detroit, Mich. 48201, U.S.A.

²Tulane University School of Medicine, New Orleans. La. 701 12. U.S.A.
Abstract

A discrete-parameter model of the human body under a variety of impact situations is developed, emphasizing the spine as the main load-carrying element. The model simultaneously accounts for axial, shear and bending deformations of the discs, the viscoelastic behavior of the discs, the variable size and mass of the vertebrae and discs, the natural curved shape of the spine, and the eccentric inertial loading caused by the head and trunk. A trapezoidal seat acceleration pulse is applied in the sagittal plane.

Numerical results generated for the pilot ejection problem, using a 10g peak acceleration pulse with finite rise time, show that bending deformations of the spinal column appreciably affect the overall body response. The effects of pulse rise time and horizontal components of acceleration are evaluated. Results are in the form of time-histories for the axial force, shear force, and moment at the disc-vertebra interfaces.
Links

DOI: 10.1016/0021-9290(71)90016-9

PubMed: 5127938

WoS: A1971I699000007
History

Received: 1970-06-11

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Cited By (40)

Year	Entry
1982	Liu YK, Krieger KW, Njus G, Ueno K, Connors M, Wakano K, Thies D. Cervical Spine Stiffness and Geometry of the Young Human Male. Wright-Patterson AFB, Ohio: Air Force Aerospace Medical Research Laboratory; November 1982. Report No. AFAMRL-TR-80-138.
1990	Dietrich M, Kedzior K, Zagrajek T. Modeling of muscle action and stability of the human spine. In: Winters JM, Woo SL-Y, eds. Multiple Muscle Systems: Biomechanics and Movement Organization. New York, NY: Springer-Verlag; 1990:451-460.
1973	Liu YK, Wickstrom JK. Estimation of the inertial property distribution of the human torso from segmented cadaveric data. In: Kenedi RM, ed. Perspectives in Biomedical Engineering: Proceedings of a Symposium Organised in Association With the Biological Engineering Society and Held in the University of Strathclyde, Glasgow, June 1972. Baltimore, MD: University Park Press; 1973:203-213.
2012	Stammen JA, Herriott R, Kang Y-S, Bolte J, Dupaix R. Sequential biomechanics of the human upper thoracic spine and pectoral girdle. In: 56th Annual Proceedings, Association for the Advancement of Automotive Medicine (AAAM). October 14-17, 2012; Seattle, WA.151-162.
1973	Williams JF, McKenzie JA. The effect of seatback stiffness and collision severity on the dynamic behaviour of the head during “whiplash”. In: Proceedings of the 1973 International IRCOBI Conference on the Biomechanics of Impact. June 26-27, 1973; Amsterdam, The Netherlands.329-338.
1997	van den Kroonenberg A, Thunnissen J, Wismans J. A human model for low-severity rear-impacts. In: Proceedings of the 1997 International IRCOBI Conference on the Biomechanics of Impact. September 24-26, 1997; Hannover, Germany.117-132.
1973	Begeman PC, King AI, Prasad P. Spinal loads resulting from -Gx acceleration. In: Proceedings of the 17th Stapp Car Crash Conference. November 17-19, 1973; Coronado, CA. Warrendale, PA: Society of Automotive Engineers:343-360. SAE 730977.
1973	Walker LB Jr, Harris EH, Pontius UR. Mass, volume, center of mass, and mass moment of inertia of head and head and neck of human body. In: Proceedings of the 17th Stapp Car Crash Conference. November 17-19, 1973; Coronado, CA. Warrendale, PA: Society of Automotive Engineers:525-537. SAE 730985.
1994	Matsushita T, Sato TB, Hirabayashi K, Fujimura S, Asazuma T, Takatori T. X-ray study of the human neck motion due to head inertia loading. In: Proceedings of the 38th Stapp Car Crash Conference. October 31–November 2, 1994; Fort Lauderdale, FL. Warrendale, PA: Society of Automotive Engineers:55-64. SAE 942208.
2012	Stammen JA, Herriott R, Kang Y-S, Dupaix R, Bolte J IV. Dynamic properties of the upper thoracic spine-pectoral girdle (UTS-PG) system and corresponding kinematics in PMHS sled tests. Stapp Car Crash J. October 2012;56:65-104.
1971	McKenzie JA, Williams JF. The dynamic behaviour of the head and cervical spine during “whiplash”. J Biomech. December 1971;4(6):477-490.
1973	Belytschko TB, Andriacchi TP, Schultz AB, Galante JO. Analog studies of forces in the human spine: computational techniques. J Biomech. July 1973;6(4):361-371.
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1978	Lin HS, Lui YK, Ray G, Nikravesh P. Systems identification for material properties of the intervertebral joint. J Biomech. 1978;11(1-2):1-14.
1987	McGill SM, Norman RW. Effects of an anatomically detailed erector spinae model on L4/L5 disc compression and shear. J Biomech. 1987;20(6):591-600.
1997	Kitazaki S, Griffin MJ. A modal analysis of whole-body vertical vibration, using a finite element model of the human body. J Sound Vibrat. February 13, 1997;200(1):83-103.
1991	Panjabi MM, Duranceau J, Goel V, Oxland T, Takata K. Cervical human vertebrae: quantitative three-dimensional anatomy of the middle and lower regions. Spine. August 1991;16(8):861-869.
1991	Panjabi MM, Takata K, Goel V, Federico D, Oxland T, Duranceau J, Krag M. Thoracic human vertebrae: quantitative three-dimensional anatomy. Spine. August 1991;16(8):888-901.
1993	Nightingale RW. The Dynamics of Head and Cervical Spine Impact [PhD thesis]. Duke University; 1993.
1998	Camacho DLA. Dynamic Response of the Head and Cervical Spine to Near-Vertex Head Impact: An Experimental and Computational Study [PhD thesis]. Durham, NC: Duke University; 1998.
1982	Sandover J. Measurement of the Frequency Response Characteristics of Man Exposed to Vibration [PhD thesis]. Loughborough, UK: Loughborough University of Technology; October 1982.
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1985	Yoganandan N. Mechanical Factors and the Threshold of Trauma of the Intervertebral Joint: A Finite Element Analysis With Experimental Validation [PhD thesis]. Marquette University; December 1985.
2011	Storvik SG. Development of an Experimental Model to Quantify Lumbar Spine Kinematics During Military Seat Ejection [Master's thesis]. Marquette University; August 2011.
1981	Tencer A. The Mechanical Properties of the Human Lumbar Spine [PhD thesis]. McGill University; April 1981.
1997	Duncan NA. The Mechanics of Curve Progression in Adolescent Idiopathic Scoliosis [PhD thesis]. McGill University; February 1997.
1999	Wilson SE. Analysis of the Forces on the Spine During a Fall With Application Towards Predicting Vertebral Fracture Risk [PhD thesis]. Cambridge, MA: Massachusetts Institute of Technology; June 1999.
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2002	Giacomin JA. An Experimental Investigation of the Vibrational Comfort of Child Safety Seats [PhD thesis]. University of Sheffield; December 2002.
1999	Matsumoto Y. Dynamic Response of Standing and Seated Persons to Whole-Body Vibration: Principal Resonance of the Body [PhD thesis]. Southampton, England: University of Southampton; June 1999.
1985	Deng Y-C. Human Head Neck Upper-Torso Model Response to Dynamic Loading [PhD thesis]. Berkeley, CA: Berkeley, University of California; 1985.
1974	Andriacchi TP. A Model for Studies of Mechanical Interactions Between the Human Spine and Rib Cage [PhD thesis]. University of Illinois at Chicago Circle; February 1974.
2001	Mazuchowski EL II. Investigation of the Biomechanical Properties of the Human Spinal Cord and Its Connective Tissue [PhD thesis]. Philadelphia, PA: University of Pennsylvania; 2001.
2012	Vette A-H. Trunk Stability During Postural Control: Tool Development and Analysis [PhD thesis]. University of Toronto; 2012.
1993	Cholewicki J. Mechanical Stability of the in Vivo Lumbar Spine [PhD thesis]. University of Waterloo; 1993.
1973	Prasad P. The Dynamic Response of the Spine During +G_Z Acceleration [PhD thesis]. Detroit, MI: Wayne State University; 1973.
1977	Begeman PC. The Effect of Energy Absorbing Devices on Spinal Loads Resulting from -G_X Acceleration [PhD thesis]. Detroit, MI: Wayne State University; 1977.
2023	Pietsch HA. Comparison of the Dynamic Response and Fracture Characteristics of Female and Male Lumbar Spine and Pelvis in Underbody Blast Loading [PhD thesis]. Detroit, MI: Wayne State University; December 2023.
1989	Crisco JJ III. The Biomechanical Stability of the Human Lumbar Spine: Experimental and Theoretical Investigations [PhD thesis]. Yale University; May 1989.