Importance of Nonlinear and Multivariable Flexibility Coefficients in the Prediction of Human Cervical Spine Motion

[+] Author and Article Information
Beth A. Winkelstein, Barry S. Myers

Department of Biomedical Engineering, Division of Orthopaedic Surgery, Duke University, Durham, N.C. 27708

J Biomech Eng 124(5), 504-511 (Sep 30, 2002) (8 pages) doi:10.1115/1.1504098 History: Received January 01, 2002; Revised June 01, 2002; Online September 30, 2002
Copyright © 2002 by ASME
Your Session has timed out. Please sign back in to continue.


Camacho, D. L., Nightingale, R. W., Robinette, J. J., Vanguri, S. K., Coates, D. J., and Myers, B. S., 1997, “Experimental Flexibility Measurements for the Development of a Computational Head-Neck Model Validated for Near-Vertex Head Impact,” Proceedings of the 41st Annual Stapp Car Crash Conference, pp. 473–486.
de Jager, M., Sauren, A., Thunnissen, J., and Wismans, J., 1994, “A Three-Dimensional Head-Neck Model: Validation for Frontal and Lateral Impacts,” Proceedings of the 38th Annual Stapp Car Crash Conference, pp. 93–109.
Deng,  Y. C., and Goldsmith,  W., 1987, “Response of a Human Head/Neck/Upper-Torso Replica to Dynamic Loading-II. Analytical/Numerical Model,” J. Biomech., 20, pp. 487–497.
Panjabi,  M. M., Brand,  R. A., and White,  A. A., 1976, “Three-Dimensional Flexibility and Stiffness Properties of the Human Thoracic Spine,” J. Biomech., 9, pp. 185–192.
Van Ee, C. A., Nightingale, R. W., Camacho, D. L. A., Chancey, V. C., Knaub, K. E., Sun, E., and Myers, B. S., 2000, “Tensile Properties of the Human Muscular and Ligamentous Cervical Spine,” Proceedings of the 44th Annual Stapp Car Crash Conference, pp. 85–102.
Moroney,  S. P., Schultz,  A. B., Miller,  J. A. A., and Andersson,  G. B. J., 1988, “Load-Displacement Properties of Lower Cervical Spine Motion Segments,” J. Biomech., 21, 9, pp. 769–779.
Myers,  B. S., McElhaney,  J. H., Doherty,  B. J., Paver,  J. G., and Gray,  L., 1991, “The Role of Torsion in Cervical Spine Trauma,” Spine, 16, pp. 870–874.
Raynor,  R. B., Moskovich,  R., Zidel,  P., and Pugh,  J., 1987, “Alterations in Primary and Coupled Neck Motions after Facetectomy,” Neurosurgery, 21, pp. 681–687.
Shea,  M., Edwards,  W. T., White,  A. A., and Hayes,  W. C., 1991, “Variation of Stiffness and Strength Along the Human Cervical Spine,” J. Biomech., 24, pp. 95–107.
Wismans, J., and Spenny, C. H., 1984, “Head-Neck Response in Frontal Flexion,” Proceedings of the 28th Annual Stapp Car Crash Conference, pp. 161–171.
Thunnissen, J., Wismans, J., Ewing, C. L., and Thomas, D. J., 1995, “Human Volunteer Head-Neck Response in Frontal Flexion: A New Analysis,” Proceedings of the 39th Annual Stapp Car Crash Conference, pp. 439–460.
Wismans, J., and Spenny, C. H., 1983, “Performance Requirements for Mechanical Neck in Lateral Flexion,” Proceedings of the 27th Annual Stapp Car Crash Conference, pp. 137–148.
Wismans, J., van Oorschot, H., and Woltring, H. J., 1986, “Omni-Directional Human Head-Neck Response,” Proceedings of the 30th Annual Stapp Car Crash Conference, pp. 313–331.
Berkson,  M. H., Nachemson,  A., and Schultz,  A. B., 1979, “Mechanical Properties of Human Lumbar Spine Motion Segments-Part II: Responses in Compression and Shear: Influence of Gross Morphology,” J. Biomech. Eng., 101, pp. 53–57.
Edwards,  W. T., Hayes,  W. C., Posner,  I., White,  A. A., and Mann,  R. W., 1987, “Variation in Lumbar Spine Stiffness with Load,” J. Biomech. Eng., 109, pp. 35–42.
Panjabi,  M. M., Summers,  D. J., Pelker,  R. P., Videman,  T., Friedlaender,  G. E., and Southwick,  W. O., 1986, “Three-Dimensional Load-Displacement Curves due to Forces on the Cervical Spine,” J. Orthop. Res., 4, pp. 152–161.
Schultz,  A. B., Warwick,  D. N., Berkson,  M. H., and Nachemson,  A., 1979, “Mechanical Properties of Human Lumbar Spine Motion Segments—Part I: Responses in Flexion, Extension, Lateral Bending, and Torsion,” J. Biomech. Eng., 101, pp. 46–52.
Panjabi,  M. M., Crisco,  J. J., Vasavada,  A., Oda,  T., Cholewicki,  J., Nibu,  K., Shin,  E., 2001, “Mechanical Properties of the Human Cervical Spine as Shown by Three-Dimensional Load-Displacement Curves,” Spine, 26, pp. 2692–2700.
Adams,  L. P., 1981, “X-ray Stereo Photogrammetry Locating the Precise, Three-Dimensional Positions of Image Points,” Med. Biol. Eng. Comput., 19, pp. 569–578.
Veldpaus,  F. E., Woltring,  H. J., and Dortmans,  L. J. M. G., 1988, “A Least-Squares Algorithm for the Equiform Transformation from Spatial Marker Coordinates,” J. Biomech., 21, pp. 45–54.
Woltring,  H. J., 1980, “Planar Control in Multi-Camera Calibration for 3-D Gait Studies,” J. Biomech., 13, pp. 39–48.
Woltring,  H. J., 1991, “Representation and Calculation of 3-D Joint Movement,” Human Movement Science, 10, pp. 603–616.
Fung, Y. C. B., Perrone, N., and Anliker, M., 1972, Biomechanics: Its Foundations and Objectives, Prentice-Hall, Inc., New Jersey.
Simon,  B. R., Coats,  R. S., and Woo,  S. L. Y., 1984, “Relaxation and Creep Quasilinear Viscoelastic Models for Normal Articular Cartilage,” J. Biomech. Eng., 106, pp. 159–164.
Winkelstein,  B. A., Nightingale,  R. W., Richardson,  W. J., and Myers,  B. S., 2000, “The Cervical Facet Capsule and its Role in Whiplash Injury: A Biomechanical Investigation,” Spine, 25, pp. 1239–1246.
Liu, Y. K., Krieger, K. W., Njus, G., Ueno, K., Connors, M. P., Wakano, K., and Thies, D., 1982, “Cervical Spine Stiffness and Geometry of the Young Human Male,” AFAMRL-TR-80-138, Air Force Aerospace Medical Research Laboratory.
Goel,  V. K., Clark,  C. R., McGowan,  D., and Goyal,  S., 1984, “An In-Vitro Study of the Kinematics of the Normal, Injured and Stabilized Cervical Spine,” J. Biomech., 17, pp. 363–376.
Yang, K. H., Begeman, P. C., Muser, M., and Niederer, P., 1997, “On the Role of the Cervical Facet Joints in Rear End Impact Neck Injury Mechanisms,” Proceedings of the International Congress & Exposition, Society of Automotive Engineers, Inc., SAE Paper #970497, pp. 127–129.
Lysell,  E., 1969, “Motion in the Cervical Spine,” Acta Orthop. Scand., 123, pp. 5–61.
Siegmund,  G. P., Myers,  B. S., Davis,  M. B., Bohnet,  H. F., and Winkelstein,  B. A., 2001, “Mechanical Evidence of Cervical Facet Capsule Injury During Whiplash: A Cadaveric Study using Combined Shear, Compression and Extension Loading,” Spine, 26, pp. 2095–2101.


Grahic Jump Location
Schematic showing the local coordinate system of a vertebra, with its origin (O) at the center of the anterior face. Also illustrated are the axes orientations (x,y,z) for the local coordinate system. As shown, the positive X-axis is oriented anteriorly along the anterior-posterior direction.
Grahic Jump Location
Schematic diagram showing the flexibility frame with bending moment applicator. The test frame is equipped with a load cell, moment and force applicators, and stereoimaging cameras for motion tracking. Also shown in this illustration is the orientation of the global coordinate system.
Grahic Jump Location
Shown is a representative nonlinear approximation (filled circles) of the measured (open circles) response curve for a typical specimen, illustrating the use of five piecewise linear functions to characterize the nonlinear response. Also shown in this plot is the closeness of the linear fits to the logarithmic description of the response.
Grahic Jump Location
(a) Shown are the primary (flexion angle) and coupled motion responses for an imposed flexion moment on a neutral specimen. The upper plot shows the rotational components and the lower plot demonstrates the coupled translations. These results illustrate the effects of loading in the sagittal plane, producing small lateral translations (y) and bending and axial torsion rotations. (b) Primary and coupled motion response magnitudes for a posteroanterior (+x) shear force applied to a representative neutral specimen.
Grahic Jump Location
Sagittal plane displacement components for a typical specimen. The sagittal plane experimental validation data, as well as the predicted motions from the three matrix models, are shown. For flexion in particular, the improved performance of the multivariable model is evident over the linear and piecewise models. For simplicity, the sagittal plane components of motion are shown as a function of applied flexion moment.
Grahic Jump Location
Lateral displacement components for a typical specimen (same as in Fig. 5) are shown as a function of the applied lateral bending moment from the validation experiment. These plots indicate the failure of the linear model to predict the motions out of the sagittal plane well.
Grahic Jump Location
RMS errors for the different models in their prediction of angular rotations. Here errors are represented as a percentage of the corresponding range of motion in each direction. The similar improvements for the piecewise and multivariable models over the linear one are observed for each motion component.




Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In