## 2 Materials and Methods
### Deltoid Segmentation Model  
Pre-operative CT images of patients who underwent shoulder arthroplasty were collected from an IRB-approved multi-center clinical outcome database of a single-platform shoulder prosthesis (Equinoxe, Exactech, Inc., Gainesville, FL, USA). All patients enrolled in this IRB-approved study provided informed consent. Inclusion criteria included primary arthroplasty with diagnoses of osteoarthritis, rotator cuff arthropathy, or rotator cuff tear. Additionally, each patient's CT scan must include complete acquisition of the deltoid muscle and scapular bone. Patients with CT images that included a metal artifact were excluded. All CT images were acquired using the ExactechGPS acquisition protocol. This CT protocol permits CT image slice thicknesses between 0.3 and 1.25 mm, with a recommended thickness of 0.625 mm and pixel resolutions between 0.3 \(\times\) 0.3 mm to 1 \(\times\) 1 mm. Additionally, this acquisition protocol permits CT images using multiple different convolution kernels from different CT manufacturers, including (but not limited to) BONE (GE Healthcare, Chicago, IL, USA), B41 (Siemens Healthineers, Erlangen, Germany), and FC30 (Toshiba/Canon Medical, Tustin, CA, USA). Please refer to Table 1 for additional information. \begin{table}
\begin{tabular}{c c} \hline \hline  & **Considered Populations** \\ \hline \multicolumn{2}{c}{**Patient Variable**} \\ \hline Gender & [M, F] \\ \hline Age cohort & \textless{}60, 60–70, 70–80, \textgreater{}80 \\ \hline Diagnosis & [OA, RCA, RCT] \\ \hline \multicolumn{2}{c}{**Image Variable**} \\ \hline Kernels * & [Bone, Bone+, Fc130, [131, 3], B60] \\ \hline Manufacturer * & [GE, Siemens, Toshiba] \\ \hline \multicolumn{2}{c}{**Exclusion Criteria**} \\ \hline Included in training process & None \\ \hline Deltoid insertion cut off & None \\ \hline Metal artifact around shoulder & None \\ \hline Low image quality & None \\ \hline Other diagnoses (fracture, ON, RA, PTA) ** & None \\ \hline Revision (shoulder) & None \\ \hline Image with pixel size & Smaller than 0.3 and larger than 1 mm \\ \hline \hline \end{tabular}
* Most five frequent kernels in our database. ** Patients with indicated diagnosis are excluded due to low prevalence.  
\end{table} 
Table 1: Patient and imaging variables included/excluded in this study. Deltoid masks were manually annotated by technicians with knowledge of shoulder anatomy using 3D slicer software (version 5.4.0; [[https://www.slicer.org](https://www.slicer.org)]([https://www.slicer.org](https://www.slicer.org)), 10 th May 2025) under the supervision of an experienced shoulder surgeon. These manually segmented masks served as training data for the ML-based auto-segmentation algorithm. An iterative batch-based human-in-the-loop approach was adopted for mask generation and model training. The process started with creating initial deltoid masks that were manually segmented for 60 patients. Next, a segmentation model was trained and used to create a new batch of masks for the remaining cases, which then underwent a correction process carried out by the technicians. These deltoid masks were then used as training data for additional iterations of the auto-segmentation ML model. In each iteration, the model was assessed using quantitative and qualitative assessments; specifically, model performance was quantified by the Dice coefficient, which quantified the similarity/voxel overlap between the predicted deltoid model and the ground truth generated by the technician. Iterative training continued until the model achieved a Dice coefficient of >0.90 on the internal test dataset. We used a pre-trained model, SwinUnetR [25], which utilizes a U-shaped network with a Swin transformer as the encoder and connects it to a CNN-based decoder, to auto-segment the deltoid. Data were split by a ratio of 80:20 for training and internal testing cohorts. The CT-scans underwent multiple augmentation sequences, including flipping, with a probability of 0.5 for all three axes and shifts in intensity in the range [\(-\)0.1, 0.1].