A THEORETICAL KINEMATIC ANALYSIS OF SLIDING CORE DISC ARTHROPLASTY DEVICES

Abstract

Introduction: Total disc arthroplasty’s (TDA) fall into two groups – constrained ball and socket and sliding core devices. It is commonly theorized that sliding core devices offer the advantage of being able to adapt to varying centres of rotation (COR) of the functional spinal unit (FSU), however no rigorous justification has, so far, been tendered for this. Despite the perceived advantage, differing clinical results have been reported in the lumbar spine, possibly with better results with ball and socket devices. Furthermore abnormal motion with a large hysteresis effect has been identified in in vitro flexibility testing with a physiological preload in the lumbar spine. The purpose of this paper was to develop an understanding of the kinematics of sliding core TDA’s, their ability to match variable COR’s of a normal FSU, and to gain an understanding of theoretical load displacement behaviour when implanted.

Methods: The motion of a biconvex sliding core prosthesis was observed to define the motion as a linked kinematic chain. By the use of sequential multiplication by appropriate transformation matrices that described this kinematic chain, equations for the position and orientation of the upper vertebrae were established. By a similar method equations for the position and orientation of the upper vertebrae were developed for a physiological simple rotation around the FSU COR. Attempts were made to solve these two sets of equations simultaneously to see if motion of the biconvex core prosthesis could match either the position, orientation or both position and orientation of the normal physiological motion. Functions defining the length of the load vector through the COR were obtained. By considering a physiological load in the direction of this vector, a function describing potential energy was defined. This was further modified by the addition of ligament constraints with a “J” shaped non linear load displacement behaviour that approximated normal ligament stiffness. Sensitivity analysis was then performed to establish the behaviour of the prosthesis under differing loads, ligament strains and malplacements and the outcomes were compared to published in vitro results.

Results: The motion of the device could be modeled as a ‘two bar linkage’. Attempts to find simultaneous solutions for the equations for the two bar linkage and physiological movement showed that a solution was possible when matching either position or orientation but not both. The biconvex core prosthesis best approximated the normal motion by a change in the length of the vector joining the FSU COR to the vertebrae above. When the potential energy caused by this change in length was plotted as a two dimensional surface, a ‘saddle shape’, indicating an unstable high energy equilibrium position at neutral was found. The addition of functions to simulate ligament structures showed a ‘metastable’ energy surface with two stable minimum equilibrium positions with an intervening unstable high energy equilibrium position. Sensitivity analysis showed that the prosthesis could adapt quite well to changes in vertical position of the FSU COR though had limited ability to adapt to anteroposterior malplacement.

Discussion: The theoretical potential energy function for a biconvex core prosthesis predicts significant hysteresis with a high energy unstable central position. The equations predict abnormal load behaviour that is similar to observed in vitro testing. This may explain the difference in clinical results.