A predictive method for estimating the glenohumeral joint center from palpable landmarks using multiple linear regression trained on CT data

Abstract

Human motion analysis often relies on skin markers to define local reference frames for tracking the movement of body segments. For the humerus, defining its local reference frame requires estimating the glenohumeral joint rotation center (GH-r), which is not directly palpable. Multiple linear regression models have been developed to estimate the GH-r from palpable landmarks, but they present limitations that affect their performance. The objective of this study was to develop a linear regression model that improves GH-r estimation from palpable landmarks and addresses key shortcomings of existing approaches. A dataset of 73 CT scans was divided into training, validation, and test sets using a 60:20:20 ratio. Several linear regression models were constructed using different algorithms, with 4 scapular skin landmarks digitized from the CT scans and subject characteristics as predictors, and the GH-r coordinates as dependent variables. The ground-truth GH-r was estimated through spherical fitting of the humeral head. The final regression model, selected for its favorable balance between accuracy and simplicity, achieved a mean Euclidean distance error (EDE) of 6.81 mm on the test set, representing a reduction of at least 10.73 mm compared to established predictive models of the GH-r applied to the same dataset, a difference that was statistically significant (p < 0.001). Sensitivity analyses to marker placement variability showed an increase in mean EDE up to 8.46 mm, still well below the errors obtained for the other literature models. Overall, the model’s performance was not markedly affected by the observed inter-observer variability, further supporting its advantages.