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 degrees 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 degrees 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.