In vivo estimation of the glenohumeral joint rotation center from scapular bony landmarks by linear regression

In this paper, a method is described for in vivo prediction of the glenohumeral joint rotation center (GH-r), necessary for the construction of a humerus local coordinate system in shoulder kinematic studies. The three-dimensional positions of five scapula bony landmarks as well as a large number of data points on the surface of the glenoid and humeral head were collected at 36 sets of cadaver scapulae and adjacent humeri. The position of GH-r in each scapula was estimated by mathematically fitting spheres to the glenoid and humeral head. GH-r prediction from scapula geometry parameters by linear regression resulted in a RMSE between measured and predicted GH-r of 2.32 mm for the x-coordinate, 2.69 mm for the y-coordinate and 3.04 mm for the z-coordinate. Application in vivo revealed a random humerus orientation error due to measurement inaccuracies of 1.35, 0.29 and 1.26° standard deviation per rotation angle. The estimated total humerus orientation error including the offset error due to the regression model inaccuracy was 2.86, 0.84 and 2.69° standard deviation. As these errors were about 15 and 20% of, respectively, the intra- and inter-subject variability of the humerus orientations measured, it is concluded that the method described in this paper allows for an adequate construction of a humerus local coordinate system.