## 2 Materials and Methods
### Expert Validation  
To gain a more comprehensive understanding of the deltoid model's performance, the segmentation algorithm was further evaluated by three shoulder surgeon experts. Specifically, the purposes of this validation were as follows: (a) to assess the clinical acceptance rate of the ML-generated deltoid masks, (b) perform a correction if the ML mask did not completely contain the full deltoid muscle or if the ML mask included any tissue other than the deltoid, (c) quantify segmentation and error between ML-generated and surgeon-corrected masks, and (d) test the non-inferiority of ML-generated masks relative to the surgeon-corrected masks compared to inter-surgeon variations. The CT scans in the validation study were randomly selected from the same multicenter clinical outcomes database of shoulder arthroplasty patients from which the training data was derived. To ensure diversity and adequate sub-group representation, we implemented a stratified random sampling strategy. Patients were grouped by key demographic variables (i.e., age, gender, diagnosis, and treatment) and image-specific variables (image kernels, CT scan manufacturer), and then randomly sampled within each group to include at least three patients per demographic and image category. \begin{table}
\begin{tabular}{c c c} \hline  & **Internal** & **External** \\  & **Development** & **Validation** \\ \hline Patients & 97 (100\%) & 32 (100\%) \\ \hline Male & 28 (29\%) & 15 (47\%) \\ \hline Female & 69 (71\%) & 17 (53\%) \\ \hline Age & & \\ \hline \textless{}60 & 7 (7\%) & 7 (22\%) \\ \hline \textgreater{}60 and \textless{}70 & 36(37\%) & 15 (47\%) \\ \hline \textgreater{}70 and \textless{}80 & 45 (46\%) & 6 (19\%) \\ \hline \textgreater{}80 & 9 (9\%) & 4 (13\%) \\ \hline Diagnosis & & \\ \hline OA & 61 (63\%) & 25 (78\%) \\ \hline RCA & 30 (31\%) & 5 (16\%) \\ \hline RCT & 24 (25\%) & 6 (19\%) \\ \hline Device & & \\ \hline aTSA & 17 (18\%) & 10 (31\%) \\ \hline rTSA & 80 (82\%) & 22 (69\%) \\ \hline Kernel & & \\ \hline Bone & 52 (54\%) & 10 (31\%) \\ \hline BonePlus & 8 (8\%) & 6 (19\%) \\ \hline FC30 & 16 (16\%) & 7 (22\%) \\ \hline \textbackslash{}[T31s^{\prime}, 3^{\prime}] & 2 (2\%) & 6 (19\%) \\ \hline B60s & 17 (18\%) & 3 (9\%) \\ \hline Standard & 2 (2\%) & \\ \hline Scanner Manufacturer & & \\ \hline Toshiba & 16 (16\%) & 7 (22\%) \\ \hline Siemens & 19 (20\%) & 9 (28\%) \\ \hline GE & 62 (64\%) & 16 (50\%) \\ \hline \end{tabular}
\end{table} 
Table 2: Summary of patients included in training and clinical validation. A total of 32 patients were selected for expert shoulder surgeon validation. The selected cases underwent review to ensure they were not part of the training process and to confirm compliance with the above-mentioned inclusion criteria. The majority of patients were diagnosed with osteoarthritis, followed by rotator cuff arthropathy, and then rotator cuff tear, and 53% of the selected cases were female. Patients underwent imaging, with the devices used coming from several different CT scanner manufacturers (50% GE, 28% Siemens, and 22% Toshiba). Please refer to Table 2 for additional information related to the patient and imaging parameters used in the external validation dataset. Three fellowship-trained shoulder surgeons and three technicians with experience in the manual segmentation of medical images participated in this validation study. The masks and the respective CT images were randomly distributed among surgeons, such that each surgeon reviewed about 20 cases, and each case was reviewed by at least two surgeons. Each mask evaluation required each surgeon to answer two questions: (1) Is the quality of the segmented mask clinically acceptable? (2) Does the mask benefit from minor or major corrections? A minor correction was required when a small segment of the ML-generated deltoid mask did not align with the deltoid boundary on a few slices, whereas a major correction was required when a large segment of the ML-generated deltoid mask did not align with the deltoid boundary on multiple slices.