# Revisiting the Role of Knee External Rotation in Non-Contact ACL Mechanism of Injury
## 2 Methods  
The knee FEM model used in this study was adapted from the Open Knee Project [36], a valuable resource promoting scientific developments that is freely available. The model geometry was obtained from the MRI of a cadaveric body donation. The tri-dimensional right knee joint parts included in this work were the bones (femur and tibia), articular cartilages (femoral and tibial, lateral and medial), ligaments (anterior, posterior, medial and lateral) and mensics (lateral and medial). All the structures were assembled according to their anatomic location. The femur and tibia were considered rigid bodies. A reference point was assigned to each of the bones to control their translational and rotational degrees of freedom. The articular cartilages were considered tied to the bones. A frictionless contact interaction was established between the menisci and the articular cartilages. Traction-only truss elements (E = 260 MPa, \(\
u\) = 0.4 and cross-sectional area of 2 mm\({}^{2}\)) were added to the menisci (Figure 1) to simulate the ligaments in the horns of the menisci. The ACL was recreated from the ground up to improve and finetune its modelling features. The ACL was defined as close to real as possible, including accurate footprint locations and a global structure that contains the anteromedial (AM) and posterolateral (PL) bundles and the surrounding connective tissue. To build the new ligament, the geometry was first defined, and then, the mesh was assigned to the structure. The ACL geometric model was designed according to the femoral and tibial footprint locations measured in the anatomical work of [PERSON] et al. [37]. All the proportions were applied to fit the  
Figure 1: Tibia, tibial cartilage, menisci and menisci ligaments. open knee model dimensions, and the created sections are represented in yellow at their final location in Figure 2.  
Six sections containing the edges of the bundles were defined between the two footprints (Supplement 1) based on the data from previous studies on the ACL anatomical dimensions [38; 39]. All the sections were merged to shape the bundles, as shown in Figure 3a. The six ACL sections were built from five cross-sectional points based on previous MRI data [40]. Based on the presented geometry, all three ACL components were meshed (AM bundle, AL bundle and connective tissue). The ACL geometry was built using Rhinoceros software, and the simulations were performed with Abaqus-2020. The ACL model was built using two distinct bundles (AM and PL), represented in dark and light blue, respectively, in Figure 3a, and the surrounding connective tissue represented in greyish. The FEM mesh for the bundles was obtained using a sweep technique, which allowed for the use of hexahedral elements along their length. The usage of this type of element has several advantages and facilitates the definition of the HGO fibre directions. For the bundles' connective tissue, a general technique was used based on tetrahedral elements. Figure 3: (**a**) Geometry of the AM and PL bundles, (**b**) Complete ACL mesh (bundles and connective tissue). Figure 2: ACL insertion dimensions in the model, (**a**) femoral, (**b**) tibial. For the surrounding connective tissue, due to its geometry, it was not possible to create a suitable hexahedral based finite element mesh, and therefore, a general technique using tetrahedral elements was used. The mesh was defined by 3000 linear hexahedral elements (Abaqus-C3D8H) in the AM and PL bundles and 3875 linear tetrahedral (Abaqus-C3D4) elements in the surrounding tissue (Figure 3b). The interfaces between the bundles and the connective tissue were defined and considered tied in order to maintain their position during the simulation. A soft hyperelastic material was used to model the connective tissue. Although a rupture of the connective tissue would expose the bundles, which would represent a risk factor for an eventual next failure of the ACL, the focus of the current work is on the bundles of the ACL.