Statistical analysis of the three dimensional joint complex

Abstract

Although three-dimensional data capture has become routine, statistical methods that take appropriate advantage of these multivariate data have not been widely developed. Researchers frequently rely on multiple isolated univariate statistical methods in the analysis of a joint's several axes of rotation and their associated motions. This approach reflects an inherent flaw in that it fails to appreciate the unbreakable link among these descriptors. We propose a new analytical perspective. Borrowing from the techniques of geometric morphometrics, data that describe multiple joint axis orientations and the motions about them are converted into a shape, an axis triangle, that is viewable in a three-dimensional space. In this format, multivariate statistical analyses can be conducted using conventional analytical packages. The axis triangle technique represents a significant advance over current analytical approaches in that it provides an encompassing method of appreciating joint rotations, as well as comprehensive consideration of joint function by linking rotational axis orientations with associated motion patterns.

Keywords:

• multivariate statistics
• oblique axes
• rotational movement
• geometric morphometrics
• axis triangle

Acknowledgements

We thank Abdulaziz Elfessi, University of Wisconsin - La Crosse Mathematics Department, for statistical consultation and advice. We thank Thomas W. Kernozek, University of Wisconsin - La Crosse Department of Health Professions, for providing comments on an early draft of this manuscript. We are also grateful to the participants of the Iowa State University Geometric Morphometrics Workshop and the membership of Morphmet.org for inspiration, instruction, and advice concerning the techniques of geometric morphometrics. Finally, we thank our reviewers for their comments and observations, which have been very useful in improving the quality of the manuscript. This manuscript is presentation #8 of the FibStR research project.