## 4 Discussion  
The objective of our work was to investigate how the muscle contractions occurring during walking affect the knee ligaments tension. The problem is of interest because of its implications with surgery planning (ligaments reconstruction and knee joint arthroplasty) and rehabilitation (recovery of muscle force, compensation strategies and orthoses). Although the role of these ligaments is well established in general terms [34], only a few publications deal with knee ligaments behavior in living subjects and dynamic conditions, [22; 23; 35; 47; 48; 49] and only one, to our knowledge, presents an estimation of the tension of the ligaments along a stride cycle, based on a musculoskeletal model [27]. The reason could be related to the complex structure of the knee joint and to the difficulty to predict the real loading conditions. Our musculoskeletal model represents a compromise between the need to represent that structure in deep detail and the need to realize a flexible tool that can simulate different functioning conditions. The performance of the model was relatively good. Even if the tibio-femoral contact force predicted by our model was larger than the force measured by an instrumented prosthesis [15; 16; 50], the main features were well reproduced. About the amplitude, it must be considered that our input data are from a different source, and probably, the anthropometric parameters and the walking velocity were different. In fact, after downscaling the absolute values, the RMS of the difference with respect to reference data was 318 N. Let us consider that the winners of the Grand Challenge competition [17] estimated the tibio-femoral contact forces with a RMS in the range from 229 N to 312 N for medial contact force and from 238 N to 326 N for lateral contact force. The main limits of our model are the lack of an interface between bone surfaces representing the cartilage and the menisci, the simple representation of the patellofemoral joint and the difficulty to adapt the model to different sizes, mainly because the repositioning of the ligaments is a very delicate procedure. Therefore, at present, it can be considered a generic model that hardly could become subject specific as it would be desirable. As to the muscle forces that are inputted to the model, different optimization approaches could have been used. Most of them are based on hypotheses about the motor control  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & & \multicolumn{2}{c}{**NoQuad**} & \multicolumn{2}{c}{**NoQuad**} & \multicolumn{2}{c}{**NoHam**} & \multicolumn{2}{c}{**NoGas**} \\  & & \multicolumn{2}{c}{**Load Acceptance**} & \multicolumn{2}{c}{**Knee Flexion**} & \multicolumn{2}{c}{**Knee Breaking**} & \multicolumn{2}{c}{**Support Phase**} \\ \hline  & & **Negative** & **Positive** & **Negative** & **Positive** & **Negative** & **Positive** & **Negative** & **Positive** \\ \hline ACL & & \(-\)63.89 & 0.30 & \(-\)57.08 & 1.35 & \(-\)0.47 & 27.25 & \(-\)18.90 & 14.14 \\  & ACL\(-\)a & \(-\)29.60 & 0.16 & \(-\)35.63 & 1.28 & \(-\)0.21 & 14.42 & \(-\)9.28 & 7.00 \\  & ACL\(-\)p & \(-\)32.55 & 0.18 & \(-\)22.59 & 0.67 & \(-\)0.31 & 12.17 & \(-\)9.71 & 7.24 \\ PCL & & \(-\)6.80 & 62.57 & - & 88.75 & \(-\)214.39 & - & \(-\)0.74 & 23.77 \\  & PCL\(-\)a & \(-\)1.22 & 18.67 & - & 26.51 & \(-\)103.83 & 0.52 & \(-\)0.78 & 5.54 \\  & PCL\(-\)p & \(-\)4.78 & 47.48 & - & 62.25 & \(-\)118.84 & 0.56 & \(-\)0.22 & 19.16 \\ LCL & & \(-\)5.39 & 24.57 & \(-\)19.92 & 1.92 & \(-\)32.9 & 3.21 & \(-\)4.54 & 21.19 \\  & LCL\(-\)1 & \(-\)1.17 & 8.24 & \(-\)5.38 & 0.57 & \(-\)13.22 & 0.59 & \(-\)0.99 & 6.72 \\  & LCL\(-\)2 & \(-\)2.32 & 8.24 & \(-\)10.92 & 0.59 & \(-\)12.83 & 0.55 &system [2; 51; 52; 53], and their results are clearly dependent on the cost function adopted and on the many parameters that have to be assumed (see [54] for an overview of the methods for muscle force prediction). For this reason, there are inconsistencies among the different authors [31; 55; 56; 57].