Arthroscopic repair of injured rotator cuff with suture anchor has become the main method for surgical treatment of rotator cuff injury. The failure of rotator cuff repair is associated with many factors, among which the failure of anchor fixation is one major cause. The reasons of the failure of anchor fixation include anchor loosening, displacement, extraction. These eventually lead to the articular cartilage damage, pain and even secondary surgery. The fixation strength of anchors is related to the design of anchors, patient's bone density, anchor insertion depth and insertion angle.At present, there is no unified opinion on the reasonable placement angle of anchor. The integrity of the repair using the anchor depends on the strength at the two main interfaces, which are the strength between the anchor and the bone and the strength between the suture and the tendon. With regard to anchor placement techniques, many orthopaedic surgeons place the anchors at the angle of 45° to the bone surface to increase the resistance of the anchor when pulled out by the tension generated by the rotator cuff. Burkhart first proposed the "Deadman theory" for the angle of anchor insertion. It is believed that the anchoring force of the anchor is the strongest when the angle of insertion is less than 45°. Therefore, in the current rotator cuff repair surgery, the surgeon usually inserts the anchor at 45° or less. But the theory was originally based on the analogy of the angular barrier stabilization system, rather than based on any biomechanical test data, some scholars have questioned this. Recent studies have shown that the "Deadman theory" does not necessarily show the strongest pull-out strength of the anchor with a suture. Nagamoto H et al placed metal anchors at 90° and 45° into artificial bones of different densities and greater tuberosity of pigs, and performed biomechanical pull-out tests. The results showed that they were placed at 90° regardless of bone density. The anchoring strength of the anchors on the surface of the bone is greater than 45°. The purpose of this study is to use three-dimensional finite element method to clarify the stress distribution pattern of suture anchor and surrounding bone inserted at different angles, and provides a theoretical basis for the selection of intraoperative insertion angle.

1. finite element modeling: (1) Objective: A thin-slice CT image of the proximal humerus and a micro-CT of a metal anchor (TwinfixTM, 5.0 mm, Smith & Nephew) were used in a patient with a rotator cuff injury (male, 68 years old, signed informed consent) . A three-dimensional model of the proximal humerus and metal anchor was established by the medical tomographic image processing software MIMICS 14.1 (Materialise, Belgium) . A cylinder with a diameter of 3.0 mm was established in the MMICICS software, and the position of the joint between the articular cartilage and the greater tuberosity opened in the foot print area of the supraspinatus tendon. The anchors were placed at 90° and 45°, and each anchor was placed in the same position and depth (the proximal end of the metal anchor was flush with the bone surface) such that the entire thread was in contact with the proximal humerus bone. The meshing function of the MIMICS software is used to mesh the 3D model. In order to simulate the shape and calculation of the metal anchor more realistically, the mesh size of the anchor is set to 0.06 mm; the proximal mesh of the humerus is given a gradient meshing method according to the shape of the model, and the mesh size interval is 0.2 mm to 0.06mm. The model is then imported into the finite element software ABAQUS 6.11, which applies the tetrahedral element to divide the model into meshes and assemble the parts as a whole. (2) Mechanical parameters of the material: The three-dimensional model of the proximal humerus was introduced into the FEA material module of the MMICICS software, and the material properties were assigned according to the gray value. According to the proximal humeral parameters provided by the software: the relationship between density and gray is ρ= 0.624 × HU + 173; the relationship between elastic modulus and density is E = 0.06 ×ρ^1.57. The proximal humerus model was introduced into ABAQUS finite element software to simulate the different densities and material properties of different parts of the proximal humerus. According to the related literature, the elastic modulus of the metal titanium alloy anchor is E=110000 MPa, and the Poisson's ratio V=0.28.Two contact pairs are defined in this finite element model: the anchor thread contact surface and the threaded contact surface created when the anchor is placed. Joint contact is defined as a finite slip, frictionless, and non-penetrating hard contact. (3) Load and boundary conditions: 6 degrees of freedom of the distal radius of the humerus is completely restrained and fixed, and the degree of freedom of the metal anchor is not restricted. A 100 N tensile load is applied to the metal anchored upper surface at different angles (15°, 30°, 45°, 60°, 75°, 90°) . The shoulder joints that simulate the rotator cuff are moved at various angles. The condition of the bone tissue and the metal anchor was measured, and the contact stress under different simulated conditions was calculated.2. statistical analysis: This study calculated the distribution of von Mises equivalent stress in the metal anchor and the bone tissue around the anchor. At the same time, the stress distribution pattern and the maximum value of the equivalent stress under different angles of traction were studied, and then the anchors were compared between 45° and 90°. Statistical analysis was performed using SPSS 16.0 (SPSS Inc., Chicago, IL, USA) . A paired t-test was used to compare the highest value of the equivalent stress between 45° and 90° anchor placement.

At different angles of 100 N tension, the maximum von mises equivalent stress of the metal anchors in all models is concentrated between the small holes below the anchor and the proximal threads. When the anchor is pulled from 15°-75°, the maximum von mises equivalent stress of the anchor placed at 45° is greater than 90°, and the difference of stress between two insertion angle decreases as the angle increases. At 90° pull load, the stress placed on the 90° anchor is slightly greater than 45°. At different angles of 100N tension, the maximum von mises equivalent stress of the bone tissue around the 45° placed metal anchor is concentrated between the proximal anchor thread and the traction side bone tissue surface; and for the 90° placed metal anchor, the maximum von mises equivalent stress of the bone tissue around the screw is concentrated around the proximal thread, which is more obvious with the increase of the pulling angle. When a metal anchor is subjected to a 100 N tensile load from 15° to 90°, the stress placed on the bone tissue around the anchor at 45° is greater than the stress placed on the bone tissue around the anchor at 90°. Statistically, the maximum value of the equivalent stress of the screw and its surrounding bone was not statistically different between insertion angles of 45° and 90° (P=0.244, P=0.319) . However, we observed that the equivalent stress of the screw and its surrounding bone tissue was less when the metal anchor was placed at 90°.

According to the results of finite element analysis, when the metal anchor is placed at 90° on the bone surface of the rotator cuff footprint, the stress on the anchor and its surrounding bone tissue is smaller than that at 45°. We recommend repairing the rotator cuff with metal anchors placed at 90° clinically to avoid early postoperative anchor fixation failure.