## 2 Materials and Methods  
### Design and Setting  
The proposed method is designed in the following four steps, as shown in Figure 1: (1) shoulder geometric data acquisition; (2) shoulder material property representation; (3) boundary and loading condition definition for humeral motion and supraspinatus tendon loading; (4) boundary condition relaxation for humeral motion. Steps 1-3 of the proposed method have referred to the traditional shoulder modeling method and are applied to FE simulation [19]. In the first step, the geometry of the shoulder model, including bones (humerus and scapula) and soft tissues (supraspinatus tendon and labrum), is reconstructed based on medical imaging information. Material properties of cartilage are considered as those of bone according to the assumption that it does not affect the simulation results [20; 21]. Herein, the medical imaging information includes computerized tomography (CT), computerized tomography arthrogram (CTA), and magnetic resonance (MR) images. Bone models of the humerus and scapula are derived from the CT images. The soft tissue models of the supraspinatus tendon and labrum are derived from the CTA and MR images. The soft tissue models are constructed by stacking the contours extracted according to the consultation of orthopedic surgeons [22]. The medical imaging information is acquired in three planes (axial, coronal, and sagittal planes). The accuracy of the shoulder model is enhanced by combining the models represented based on three planes. In the second step, the material properties are applied to the shoulder model to represent the deformation of in vivo properties. The material properties are included in vertices of the elements consisting of shoulder models. The humeral and scapular models are assumed to be rigid body material because bone has extremely high stiffness compared to soft tissues. The material property of the labrum is modeled as linear elasticity with isotropy and homogeneity, and that of the supraspinatus tendon is modeled as hyperelasticity considering the large deformations. The material properties used in the shoulder model were referenced from the conventional literature [23; 24; 25; 26], and details are shown in Table 1.  
In the third step, the boundary and load conditions are defined to represent shoulder motion, as shown in Figure 2. The boundary condition is humeral abduction, generated based on screw motion. Generally, the screw motion is used to represent the shoulder motion based on [PERSON] theorem [27]. Because actual shoulder motion is not rotated based on spherical coordinates, it is hard to represent humeral abduction among musculoskeletal tissue. To solve this, the humeral abduction is represented as a screw motion between two postures (neutral position and abducted position). The humeral model superimposed on the scapula model among bone models was derived based on CT images scanned from the two postures, and it was used in the screw motion of the humerus. The represented humeral abduction is achieved as rotation and translation on the basis of the screw axis. The load condition is pretension pulled from the distal to proximal side of the supraspinatus tendon, and this is performed simultaneously with humeral abduction. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Feature** & **Type** & **Mechanical Properties** & **Number of Elements (Element Type)** & **Reference** \\ \hline \hline \multirow{2}{*}{Scapula} & \multirow{2}{*}{Rigid body} & \multirow{2}{*}{E = 15,000 MPa, \(\
u\) = 0.3} & 12,967 (S4R) & [23] \\ \cline{1-1} \cline{3-5} \cline{5-  
Fine modeling and motion generation are important because FE simulations are affected by geometry and motion trajectory [28]. However, an error occurred in the critical process zone of the insertion site of the supraspinatus tendon in FE simulations based on the conventional method (steps 1 to 3), as shown in Figure 3a.