A method to calculate relative spinal motion without digitization

Abstract 

Background context

Euler and projection methods have been used to describe relative spinal motion. In the Eulerian formulation, the exiting method used vector form of Euler angles and only provides an approximation. In the projection method, local coordinate systems constructed with digitization can affect the accuracy of kinematical results. A more consistent data reduction method is desired to calculate relative spinal motion (range of motion) from raw marker data.

Purpose

To develop a new data reduction method to calculate relative spinal motion based on arbitrarily oriented local coordinate systems of individual vertebrae, and to simplify experimental procedures in multidirectional testing of spines.

Study design/setting

The relative spinal motion was determined from raw marker data using transformation matrices.

Methods

In the Eulerian formulation, the relative motion of a vertebra to its subjacent level was determined using transformation matrices rather than vector operation on Euler angles. In the projection method, the projection axes were determined by tranforming local coordinate systems. Both approaches can be used to analyze raw marker data.

Results

The new data reduction method was successfully implemented to analyze the raw data acquired on an intact L1–L2 motion segment. There was little difference between the Euler method and projection methods.

Conclusions

In conclusion, an alternative data reduction method in both Euler and projection angles to calculate range of motion for in vitro spine biomechanical studies was presented. The method was validated on a human cadaveric lumbar motion segment under axial torsion, lateral bending, and flexion extension. Because the relative spinal motion does not depend on how local coordinate systems are oriented, the digitization process can be eliminated in most multidirectional flexibility tests. Compared with previous methods, this new method provides more consistent kinematical results and significantly simplifies experimental procedures.

Keywords: Multidirectional test, Transformation, Spinal motion