On the Stiffness Matrix of the Intervertebral joint application to total disk...

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From:ASME JOURNAL OF BIOMECHANICAL ENGINEERING, SUBMITTED FOR PUBLICATION 1


On the stiffness matrix of the intervertebral joint:
application to total disk replacement.
Oliver M. O’Reilly, Melodie F. Metzger, 3 Jenni M. Buckley,
4 David A. Moody and Jeffrey C. Lotz

Abstract

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 parameterize the rotation, an associated basis, which is known as the
dual Euler basis, to describe the moments, and it enables a characterization of the non-conservative nature
of the joint caused by energy loss in the poroviscoelastic disc 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 disc and compared to the matrices associated with the same segment after
the insertion of a total disc replacement system. In this manner, the matrix is used to quantify the changes
in the intervertebral kinetics associated with total disc replacements. As a result, this paper presents the
first such characterization of the kinetics of a total disc replacement.

Index Terms
Spine kinematics, intervertebral disc, stiffness matrix, disc arthroplasty.