构建肩关节有限元模型，用于分析肩袖生物力学。

采集1名26岁健康男性志愿者右肩CT、MRI数据，构建肩关节有限元模型，包含肩胛骨、肱骨、锁骨，以及肩袖肌群（冈上肌、冈下肌、小圆肌、肩胛下肌）。模拟肱骨在肩胛骨平面外展，分析肩袖肌肉应力变化。

肱骨在肩胛骨平面外展0°~30°过程中，各组肌腱与肱骨头连接处的应力均增大。冈上肌腱应力变化速率较快；肩胛骨前方的肩胛下肌对比肩胛骨后方的冈下肌-小圆肌，两组肌腱的应力变化较为同步。当肱骨在肩胛骨平面外展30°时，冈上肌腱、肩胛下肌腱及冈下肌腱-小圆肌腱与肱骨头连接面的平均应力分别为7.894 8、4.721 7、3.768 8 Mpa，冈上肌腱关节面与滑囊面结点平均应力分别为7.931 4、4.099 0 Mpa。冈上肌腱的关节面与滑囊面应力有明显差异，应力差值随肱骨在肩胛骨平面外展而增大，造成的剪切力可造成冈上肌腱撕裂。

肩袖对肩关节的活动与稳定性有重要作用，其受力特点易引起肩袖损伤。

The rotator cuff, which consists of supraspinatus, infraspinatus, teres minor and subscapularis, participates in shoulder joint motion and provides active shoulder stability. The rotator cuff tear is a common clinical problem. The tear rate is 4% in the population aged 40 to 60, and over 54% in the population over 60 years old. Among the 4.5 million patients with rotator cuff disease in the United States annually, 75,000 patients have undergone surgery. The rotator cuff tear can be caused or aggravated by acromial morphology, mechanical factors, blood supply reduction, tendon degeneration, etc. Although some scholars have used the finite element method to investigate the biomechanical mechanism of rotator cuff tear, the early model was two dimensional with simplified structure while the later is a three-dimensional model with missing rotator cuff and distorted morphology. For this reason, this study constructs a more complete finite element model of the shoulder joint, analyzes the biomechanics of rotator cuff during abduction of humerus in the scapular plane.

Ⅰ. CT and MRI data collection of shoulder complex. A 26-year-old healthy male volunteer was selected and his right shoulder (right handed) was used as the study object. The experiment was approved by the Ethics Committee of Shanghai First People’s Hospital, and the participating volunteer signed the informed consent form.In order to construct bone and soft tissue model, the right shoulder of the volunteer was scanned by CT and MRI in the supine position. The CT parameters were as follows: Slice thickness 0.625 mm, spacing between slices 0.625 mm and 512×512 pixels per layer. The MRI imaging of oblique coronal plane (parallel to supraspinatus tendon) and transverse section was performed. The MRI parameters for oblique coronal plane scanning are as follows: body coil, scan sequence SE, type 2D, layer thickness 2.5 mm, RT 4 200 ms, ET 13.4 ms, magnetic field strength 3T, layer spacing 3.5 mm, FOV 309, FA 90°, and matrix 1 024 ×1 024.Ⅱ. Geometric modeling.1. Establishment of 3D model of shoulder skeleton: The CT data was imported into Mimics Research 19.0 to establish the three-dimensional model of humerus, scapula and clavicle. The 3 bones were smoothed with the reverse engineering software Geomagic Design X to establish the shoulder skeletal 3D model. 2.Establishment of 3D model of rotator cuff:The MRI data were imported into Mimics software, and the mask of the rotator cuff muscles was manually drawn and edited according to the image, and processed with Calculate 3D. The two sets of rotator cuff models generated from MRI images of transverse section and oblique coronal data are aligned into a better quality model with the "Patch Creation Wizard" feature of Geomagic to improve the information loss caused by the thickness of the MRI single-angle imaging. 3. Model assembly: As the coordinate system of image data obtained by MRI and CT scan is different, and the spatial position is not registered, the registration was completed in Geomagic referring to the method adopted by Seong W. Jang, et al. during the construction of SLAP injury model, and the rotator cuff was optimized to a smooth object. 4. Meshing: The skeletal geometry was drawn using 2D shell element. The joint surface between the rotator cuff and the humeral head was divided with 2D mesh, and it was projected on the humeral head to ensure that the mesh of the tendon and the humeral head was consistent. A second order 10-node 4-wedge element was generated based on the rotator cuff mesh.Ⅲ.Establishment of finite element model.1.Material properties of shoulder joint: This experiment focuses on the stress of rotator cuff . Since the elastic modulus of the bone is much larger than that of the soft tissue, it is simplified to a rigid body to reduce the amount of computer calculation. According to the relevant literatures, the elastic modulus of the rotator cuff is set to 1.08 Mpa and the Poisson’s ratio is set to 0.49, while the elastic modulus of the rotator cuff tendon is 1 200 Mpa and the Poisson’s ratio is set to 0.4. 2. Boundary conditions: A "tie" bind is set at the junction of the model between the tendon and the bone structures, and the contact between humerus and glenoid is frictional (friction coefficient 0.2) . The scapula plane is defined as the plane that formed by the acromion, the subscapular angle and the superior scapular angle, and made with these 3 points in Geomagic. The glenohumeral articular surface of humeral head is fitted to the sphere, and the straight line of the sphere is made perpendicular to the plane of the scapula. This line is set as the rotation axis of humeral movement. In the experiment, the scapula and clavicle are used as the datum coordinate system, and the humerus was set abducted 30° relative to the scapular in the scapular plane. According to scapulohumeral rhythm, the humerus is abaxially 45°relative to the central axis of the body in the scapular plane .Ⅳ.Data Processing.The keyframes corresponding to the humerus abduction of 5°, 10°, 15°, 20°, 25°, and 30°are selected, and the stresses at the junction nodes between the rotator cuff and the humeral head are respectively output. In this experiment, the connection between the rotator cuff and the humeral head of each group was regarded as the whole. The difference of stress distribution on the joint surface was not considered at present, and the average value of each group was obtained by SPSS 20 software.

During the abduction of the humerus in the scapular plane, the stress of the junction between the tendons and the humeral head all increased. The change rate of supraspinatus tendon was faster, while the change rates of subscapular muscle, infraspinatus muscle and teres minor were synchronous (Pearson correlation coefficient, r = 0.997) . There was a significant difference in the stress between the articular surface and the sacral surface of the supraspinatus tendon. The stress difference increased with the abduction of the humerus in the scapular plane with a maximum of 3.832 4 Mpa. The overall trend was that the closer to the humeral head, the greater the stress, and the local stress concentration was in the critical region of the supraspinatus tendon compared with the ventral junction and the tendon insertion.

This study constructs a rotator cuff model of healthy right-handed adult male, and calculates the stress changes of various nodes through simulating the 45°abduction of the upper limb in the scapular plane of the scapula by the 30°abduction of the humerus in the scapular plane. Experiments have shown that during the abduction of the humerus in the scapular plane, there is stress concentration in the insertion of supraspinatus tendon and the critical region, which can induce rotator cuff injury. The shear force caused by the stress difference in the insertion of supraspinatus tendon may result in the articular surface tear of the tendon insertion.