0
Research Papers

On the Stiffness Matrix of the Intervertebral Joint: Application to Total Disk Replacement

[+] Author and Article Information
Oliver M. O’Reilly

Department of Mechanical Engineering, University of California at Berkeley, Berkeley, CA 94706-1740oreilly@berkeley.edu

Melodie F. Metzger, Jenni M. Buckley, Jeffrey C. Lotz

Department of Orthopaedic Surgery, University of California at San Francisco, San Francisco, CA 94110

David A. Moody

Department of Mechanical Engineering, University of California at Berkeley, Berkeley, CA 94706-1740

J Biomech Eng 131(8), 081007 (Jul 02, 2009) (9 pages) doi:10.1115/1.3148195 History: Received May 19, 2008; Revised April 17, 2009; Published July 02, 2009

The traditional method of establishing the stiffness matrix associated with an intervertebral joint is valid only for infinitesimal rotations, whereas the rotations featured in spinal motion are often finite. In the present paper, a new formulation of this stiffness matrix is presented, which is valid for finite rotations. This formulation uses Euler angles to parametrize the rotation, an associated basis, which is known as the dual Euler basis, to describe the moments, and it enables a characterization of the nonconservative nature of the joint caused by energy loss in the poroviscoelastic disk and ligamentous support structure. As an application of the formulation, the stiffness matrix of a motion segment is experimentally determined for the case of an intact intervertebral disk and compared with the matrices associated with the same segment after the insertion of a total disk replacement system. In this manner, the matrix is used to quantify the changes in the intervertebral kinetics associated with total disk replacements. As a result, this paper presents the first such characterization of the kinetics of a total disk replacement.

FIGURES IN THIS ARTICLE
<>
Copyright © 2009 by American Society of Mechanical Engineers
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Figure 1

Schematic of a motion segment consisting of a pair of vertebral bodies V1 and V2 and the intervertebral disk I. One of the pair of facet joints is also indicated, as are the bases {p1,p2,p3} for V1 and {t1,t2,t3} for V2.

Grahic Jump Location
Figure 2

Schematic of the 3-2-1 set of Euler angles: ψ, θ, and ϕ. In this figure, the vectors g1=p3, g2=t2′=cos(ψ)p2−sin(ψ)p1, and g3=t1″=cos(θ)t1′+sin(θ)p3 form the Euler basis. As illustrated in (b), the dual Euler basis {g1,g2,g3} is distinct from the Euler basis.

Grahic Jump Location
Figure 3

Schematic diagram of experimental setup: 40 deg sacral slope and 850 N load in standing position. (a) Testing device constrained L5 posture in flexion, extension, and bending for investigating L5/S1 kinematics. (b) Load is uniformly distributed and applies both shear of 550 N and compression of 650 N. In (b), the 3 deg and 6 deg wedges, which are used to achieve the desired relative motion of the vertebrae, are also shown.

Grahic Jump Location
Figure 4

The moment component M⋅p1 as a function of the angle ϕ of flexion/extension for an intact motion segment and three different positionings of a TDR. Here, and in Figs.  56, the label i stands for intact, p stands for posterior, a denotes anterior, and m denotes a centered positioning of the TDR.

Grahic Jump Location
Figure 5

The moment components (a) M⋅p2 in the lateral direction and (b) M⋅p3 in the axial direction as a function of the angle ϕ of flexion/extension for an intact motion segment and three different positionings of a TDR. The label i stands for intact, p stands for posterior, a denotes anterior, and m denotes a centered positioning of the TDR.

Grahic Jump Location
Figure 6

The values of the aggregate stiffness ratio S for the posterior (p), centered (m), and anterior (a) positionings of the TDR

Grahic Jump Location
Figure 7

A schematic drawing of an intervebral disk I between the vertebra V1 and V2. The point C of the disk I has a position vector x1+π1=x2+π2 relative to the fixed origin O. The force Fm and moment Mm shown in this figure are supplied by the load cell.

Tables

Errata

Discussions

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.

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