###### Abstract  
A musculoskeletal model was developed to analyze the tensions of the knee joint ligaments during walking and to understand how they change with changes in the muscle forces. The model included the femur, tibia, patella and all components of cruciate and collateral ligaments, quadriceps, hamstrings and gastrocnemius muscles. Inputs to the model were the muscle forces, estimated by a static optimization approach, the external loads (ground reaction forces and moments) and the knee flexion/extension movement corresponding to natural walking. The remaining rotational and translational movements were obtained as a result of the dynamic equilibrium of forces. The validation of the model was done by comparing our results with literature data. Several simulations were carried out by sequentially removing the forces of the different muscle groups. Deactivation of the quadriceps produced a decrease of tension in the anterior cruciate ligament (ACL) and an increase in the posterior cruciate ligament (PCL). By removing the hamstrings, the tension of ACL increased at the late swing phase, while the PCL force dropped to zero. Specific effects were observed also at the medial and lateral collateral ligaments. The removal of gastrocnemius muscles produced an increase of tension only on PCL and lateral collateral ligaments. These results demonstrate how musculoskeletal models can contribute to knowledge about complex biomechanical systems as the knee joint. knee joint ligaments; walking; dynamic simulation; musculoskeletal modelling; knee joint biomechanics 26 January 2021 2 March 2021 2  
The analysis of such a complex structure has been carried out by many authors through different approaches. Studies on cadaver specimens [5; 6; 7] have the advantage of dealing with the real anatomy and the real mechanical properties of tissues. However, they are difficult to realize and require special equipment to reproduce a physiological movement and to apply loads and muscle forces. On the other hand, another important approach, the \"finite elements\" method [8; 9; 10], could provide the estimation of all the structural variables in great detail, but the many uncertainties about the biological material properties and the need for an arbitrary definition of the boundary conditions pose a problem of results reliability [9; 11]. Direct quantification of in vivo knee motion can be achieved through special techniques that extract the pose of the bones from single-plane fluoroscopy [12; 13]. This technique is particularly effective for analyzing the motion of implanted knee joint prostheses [14], but its application is limited to a narrow volume of acquisition. In vivo measurement of inter-joint contact forces during locomotion and other motor acts have been obtained by implanting special instrumented joint prostheses [15; 16]. The obtained results are considered as the reference for subsequent study validations [17]. Other interesting quantities like the tension of the ligaments cannot be obtained by this method. Attempts to measure them in vivo [18; 19] have been made, but many technical and ethical problems occur with this method, and practically the only ligament deformations can be obtained. Musculoskeletal models have the potential to permit the estimation of forces internal to the joint, provided that a suitable representation of the joint structure is performed. Pioneering studies have been made by [PERSON] et al. [20] who analyzed the forces in the knee during walking. The knee was modelled as a single axis joint and in each instant along the walking cycle only a reduced number of muscles, ligaments and contact forces was assumed to be active, so that the number of unknowns was equal to the number of equilibrium equations. [PERSON] and [PERSON] [21] considered the possibility of antagonistic muscles co-contractions while computing the internal knee joint forces during walking, but their model was restrained to the sagittal plane.