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Average rotation matrices for converting scapula- and glenoid-based coordinate systems to ISB recommendations
Florent Moissenet1, Benjamin Michaud2, Pierre Puchaud3
1Kinesiology Laboratory, Geneva University Hospitals and University of Geneva, Geneva, Switzerland; Biomechanics and Translational Research in Surgery, Department of Surgery, University of Geneva, Geneva, Switzerland.
Journal of Biomechanics
|February 21, 2026
Summary
Harmonizing shoulder biomechanics data is crucial. New average rotation matrices effectively reduce discrepancies between various scapular local coordinate systems (LCSs), improving data interoperability.
Area of Science:
- Biomechanics
- Orthopedics
- Human Movement Science
Background:
- Defining bone-embedded local coordinate systems (LCSs) is essential for shoulder biomechanics research.
- Multiple scapular LCS definitions hinder data comparison and interoperability.
- Existing International Society of Biomechanics (ISB) recommendations are not universally adopted.
Purpose of the Study:
- To extend the use of average rotation matrices to 11 common scapular LCSs.
- To quantify geometric transformations between these LCSs.
- To provide a reliable method for harmonizing scapular kinematic data.
Main Methods:
- Statistical shape models from 80 participants generated 1000 scapulae.
- Computed average rotation matrices between 11 scapular LCSs and the ISB-recommended LCS.
- Assessed accuracy using helical angles.
Main Results:
- Average rotation matrices significantly reduced maximal discrepancies between LCSs from 21.9° to 5.2°.
- Scapula-based LCSs showed lower discrepancies than glenoid-based systems.
- Results demonstrated robustness across datasets and populations, with minimal differences (<3°) compared to prior work.
Conclusions:
- Average rotation matrices offer a reliable framework for harmonizing scapular kinematic data.
- This approach enhances data merging and interoperability in shoulder biomechanics.
- Facilitates consistent analysis across studies using different LCS definitions.
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