CT images of a healthy 33 years old man were used to compare forearm bone's stability and biomechanical behavior of Moradi's interosseous prosthesis(model B) with the healthy forearm(model A) under different loading conditions using the finite element method.
CT images of a healthy 33 years old man obtained from Computed Tomography were used to construct 3D geometry, including ulnar, radius, and distal Humerus. After receiving the CT images, MIMICS software (MIMICS 10.1; Materialise NV, Leuven, Belgium) was used to convert the images into STL format, which was finally imported to CATIA (CATIA V5; Dassault Systemes, Ve' Lizy-Villacoublay, France) to construct the final solid models. In this study, both trabecular and cortical bones were modelled with considering 2 mm offset toward bone from the outer surface as trabecular bone. In contrast, the cortical bone's outer surface cannot detect the cartilages as CT images. The filled gap between each bone in joints is considered the related cartilage. The final CAD files were imported into ABAQUS software (ABAQUS 6.11, Dassault Systèmes, Vélizy-Villacoublay, France), and subsequent finite element procedures were performed as the following sections. The final geometry of the model is depicted in Figure1.
A specific defect by subtracting a region from the ulna was created to insert the DRUJ prosthesis, as depicted in Figure 1. The interosseous DRUJ prosthesis is inserted between two sides of osteotomy where the pseudoarthrosis is carried out in the Sauvé-Kapandji procedure to address the drawbacks of different surgical techniques and prostheses . Also, it has two main distal and proximal parts connected with a ball. This ball enables the prosthesis to move freely in each degree of freedom. The proximal part fixes to ulna and radius with two screws. Finally, the distal and proximal stems centered on the sphere can have axial movements and bending.
All materials used for cortical and trabecula bone, cartilages, different parts of the prosthesis are considered linear elastic . Also, titanium material properties are assigned to all prosthesis parts except the ball. For the ball, polyurethane  linear elastic properties are assigned . Material properties of the bone were defined by using Young’s modulus of 17.5 GPa for the cortical bone and 309.8 GPa for the trabecular bone. The Poisson’s ratio for both the cortical and cancellous bones was 0.3. Cartilage was modelled with Young’s modulus of 12 MPa and Poisson’s ratio of 0.4 . Titanium and Polyurethane were assumed to have Young’s modulus of 110 GPa, and Poisson’s ratio was 0.35 and 0.31, respectively [18, 19].
Seven ligaments stand for tension force between bones modelled with spring elements [17, 20]. To better simulate the function of the ligaments, the number of springs assigned to each of the elbow ligaments; Medial anterior, Medial posterior, Lateral radial, Lateral ulnar, four parallel springs and were assigned stiffnesses of 72.3, 52.2, 15.5, and 57 N/mm respectively, and for the Annular ligament, three parallel springs with the stiffness of 28.5 N/mm assigned. For each distal/proximal interosseous membrane and central interosseous membrane, two springs with the stiffness of 18.9 N/mm and 65 N/mm assigned, respectively, based on the orientation reported in the study, were considered. The position of these ligaments was selected based on the references [17, 20].
Loading and boundary condition
Cortical and trabecular bones bounded together. The interface of the distal and proximal part of the prosthesis is considered bound to the bone, and frictionless contact is defined between the ball and the prosthesis. The bones and ligaments of the wrist were not considered in this study, so the proximal surface of the ulna and radius coupled together eliminated the degrees of freedom . Each ligament bonded to its bone and the frictionless surface to surface contact considered for the ligaments of humerus-radius, humerus-ulna, and radius-ulna.
Five different loading scenarios were considered for both models A and model B. These loading conditions represent different conditions each hand encounters with. These loading conditions include pronation (500, 1000, 2000, and 5000 N.mm), supination (500, 1000, 2000, and 5000 N.mm), dorsal loading (10, 30, and 50 N), volar loading (10, 30, and 50 N), and traction (100, 150, and 200 N). To simulate the supination loading, first the 180 ºrotation is applied to the Ulna and Radius with the origin depicted in Figure 2, then the torque is applied. In all simulations, the proximal surface of Humerus was fixed. All loading conditions are depicted in Figure 2.
Applying torque on the wrist in pronation and supination in the distal radius side is inserted, and the amount of torque in the joint dislocation is recorded.
Finite element analysis
ABAQUS-CAE was used to build the finite element meshes with 4-noded linear tetrahedrons. After simulating the convergence analysis to get sufficient accuracy in the results. All simulations performed with ABAQUS (ABAQUS 6.11, Dassault Systèmes, Vélizy-Villacoublay, France).