Average rotation matrices for converting scapula- and glenoid-based coordinate systems to ISB recommendations

Defining bone-embedded local coordinate systems (LCSs) is fundamental in shoulder biomechanics, yet multiple scapular LCSs exist, hindering data comparison. Although the International Society of Biomechanics (ISB) has published recommendations, alternative definitions based on distinct anatomical landmarks remain often used. To address these inconsistencies, average rotation matrices were recently proposed to convert between the three most common scapular LCSs, thereby facilitating comparison, merging, and interoperability between datasets. Building upon this, we have extended the approach to 11 scapular LCSs reported in the literature, including scapula- and glenoid-based systems. Using statistical shape models derived from 80 participants (asymptomatic and pathological shoulders), 1000 scapulae were generated to quantify geometric transformations between LCSs. Average rotation matrices were computed for each alternative system relative to the ISB-recommended LCS, and accuracy was assessed using helical angles. The application of the average rotation matrices substantially reduced the maximal discrepancies between LCSs, from 21.9° to 5.2°. Scapula-based systems exhibited lower discrepancies than glenoid-based ones, reflecting greater morphological variability in the glenoid region. Comparisons with previously published matrices showed minimal differences (