Measuring the critical shoulder angle on radiographs: an accurate and repeatable deep learning model

Purpose: Since the critical shoulder angle (CSA) is considered a risk factor for shoulder pathology and the intra- and inter-rater variabilities in its calculation are not negligible, we developed a deep learning model that calculates it automatically and accurately. Methods: We used a dataset of 8467 anteroposterior x-ray images of the shoulder annotated with 3 landmarks of interest. A Convolutional Neural Network model coupled with a spatial to numerical transform (DSNT) layer was used to predict the landmark coordinates from which the CSA was calculated. The performances were evaluated by calculating the Euclidean distance between the ground truth coordinates and the predicted ones normalized with respect to the distance between the first and the second points, and the error between the CSA angle measured by a human observer and the predicted one. Results: Regarding the normalized point distances, we obtained a median error of 2.9%, 2.5%, and 2% for the three points among the entire set. Considering CSA calculations, the median errors were 1° (standard deviation 1.2°), 0.88° (standard deviation 0.87°), and 0.99° (standard deviation 1°) for angles below 30°, between 30° and 35°, and above 35°, respectively. Discussion: These results demonstrate that the model has the potential to be used in clinical settings where the replicability is important. The reported standard error of the CSA measurement is greater than 2° that is above the median error of our model, indicating a potential accuracy sufficient to be used in a clinical setting.