# Revisiting the Role of Knee External Rotation in Non-Contact ACL Mechanism of Injury
## 2 Methods
Therefore, it was considered that the connective tissue would be able to sustain large amounts of strain. The femoral and tibial ACL sections were fixed at their respective bony footprints to mimic their native anatomical role. A surface-to-surface general contact (with default interaction, contact pair with default thickness (1.0) and adjust 0.0) between the other ligaments, cartilage, menisci and bones was also defined. The ACL bundles were modelled using the anisotropic HGO constitutive model, which takes into account the existence of the collagen fibres embedded in a soft matrix. The ACL connective tissue surrounding the bundles was modelled with the Neo-Hookean hyperelastic constitutive model. Table 1 describes all the structures comprised in the model, the constitutive models applied and the properties obtained from the literature. Several uniaxial truss elements were used to simulate other relevant structural ligaments with a role in the knee kinetics. The added structures are highlighted in Figure 4a and Video 1 and modelled based on the properties and location described by [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] (2016). The ligaments were defined with truss elements that have five elements each. The simulations were performed with the femur fixed, and all the boundary conditions (Figure 4c and Table 2) were imposed in the reference node of the tibia, node O in Figure 4c. All the boundary conditions followed the movement except one that was fixed in the initial axis direction, which was defined  
to simulate the quadricep and hamstring muscles' action with a load of 600N [43] at the y-axis, as the femur position was fixed. Figure 4b shows the full model in the anterior view with the ACL bundles' mesh highlighted in blue. Figure 4: **(a)** Posteromedial view of the truss elements representing the structural ligaments in the knee joint. The structures defined are the superficial (SM), deep (DM) and oblique (OM) bundles of the medial collateral ligament; the medial (APM), lateral (APL), oblique poplilest (APO) and arcuate poplilest (APA) bundles of the posterior capsule; the anterolateral structure (AL) and the poplite-ofibular ligament (PF); **(b)** anterior view of the FEM model with the ACL highlighted. Legend: M, medial side; L, lateral side; **(c)** Boundary conditions and loads imposed in the model: X-axis with anterior and valgus loads, Y-axis with knee flexion and Z representing the axial load IR/ER. Despite the challenge related with the validation process in FEM models, mainly in such complex structures as the knee joint as described by some authors [44; 45], an indirect validation was performed comparing the results obtained with the model developed in this study against those reported by [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] [26]. The results compared were the tibial IR, as the knee was flexed up to 50 degrees, and the strain in the ACL and medial collateral ligament (MCL) during the abduction moment. The medial and lateral meniscus displacements were compared and validated based on the data from [PERSON] et al. [46]. The results obtained achieved similar values to those reported by [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON], [PERSON] and [PERSON] [26] (Supplement 2), which led us to the next milestone. From a mechanical point of view, the goal of the present model is to be used as a reference model, which intends to represent a \"normal\" native biomechanical behaviour of the knee joint. The usage of such a model allows us to test different hypotheses. An extended analysis of the knee joint was performed with a fixed 20 degrees of knee flexion and 50 Nm of abduction moment and compared, including several combinations of different magnitudes of tibial internal and external rotations and sagittal and axial loads (Table 2). The ACL most commonly tears with a low degree of knee flexion accompanied by an axial load (e.g., landing from a jump or cutting manoeuvres) [47; 48; 49; 50; 51; 52; 53; 54].