## 2 Materials and Methods
### The Model Implementation
As a consequence, knowing the reference length in our model (\(L_{ref}\)), the rest length \(L_{0}\) was computed as  
\[L_{0}=\frac{L_{ref}}{\varepsilon_{ref}+1} \tag{2}\]  
In our simulations, we adopted the values of \(\varepsilon_{ref}\) reported in [26]. The only exception was the PCL-a for which the reported value was \(\varepsilon_{ref}=-0.21\), which appeared to be a mistake since the values for most of the other ligaments were in the range 0.02-0.06, in absolute. We assumed for this ligament the value \(\varepsilon_{ref}=-0.03\) by assuming that the ligament was slack in the reference position and would be recruited when stretched above the 3% of the reference length. According to the mentioned authors, the MCL-da was also considered slack in the reference position, with a reference strain \(\varepsilon_{ref}=-0.08\). The anterolateral capsule, not taken into account in the mentioned paper, was assumed to have a small deformation in the reference position (\(\varepsilon_{ref}=-0.002\)), considering that it will lengthen during knee flexion. All the strain values, reference lengths and rest lengths are reported in Table 1. The difference between the reference length \(L_{ref}\) and the rest length \(L_{0}\) is reported in the fifth column. The values range from 2.67 mm (MCL-i) to \(-\)3.24 mm (MCL-da). A negative value means that the ligament was slack in the reference position. As to the \(K\) parameter (stiffness in the linear section of the force-strain characteristics), the values reported by [26] were adopted in our model. For those ligaments that appeared as single units in the mentioned paper but in our model were split, the stiffness of each bundle was obtained by dividing the reported value by the number of bundles constituting \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \(\varepsilon_{ref}\) & \(L_{ref}\) (mm) & \(L_{0}\) (mm) & \(\Delta L\)=\(L_{ref}\)–\(L_{0}\) (mm) & \(K\) & \(F_{ref}\)(N) \\ \hline ACL-a & 0.02 & 35.91 & 35.21 & 0.7 & 1500 & 5.00 \\ ACL-p & 0.02 & 31.26 & 30.65 & 0.61 & 1600 & 5.33 \\ PCL-a & \(-\)0.03 & 26.19 & 27.01 & \(-\)0.82 & 2600 & 0.00 \\ PCL-p & 0.02 & 31.25 & 30.64 & 0.61 & 1900 & 6.33 \\ LCL-1 & 0.02 & 46.82 & 45.90 & 0.92 & 667 & 2.22 \\ LCL-2 & 0.02 & 40.49 & 39.70 & 0.79 & 667 & 2.22 \\ LCL-3 & 0.02 & 41.82 & 41.00 & 0.82 & 667 & 2.22 \\ MCL-a & 0.02 & 67.72 & 66.40 & 1.32 & 2500 & 8.33 \\ MCL-i & 0.04 & 69.50 & 66.83 & 2.67 & 3000 & 40.00 \\ MCL-p & 0.02 & 66.33 & 65.03 & 1.3 & 2500 & 8.33 \\ MCL-da & \(-\)0.08 & 37.20 & 40.44 & \(-\)3.24 & 2000 & 0.00 \\ MCL-dp & 0.03 & 41.00 & 39.82 & 1.18 & 4500 & 33.75 \\ CAP-Ant-L & 0.002 & 29.23 & 29.17 & 0.06 & 3518 & 0.12 \\ CAP-Post-L & 0.06 & 37.70 & 35.57 & 2.13 & 1500 & 45.00 \\ CAP-Post-M & 0.06 & 36.78 & 34.70 & 2.08 & 1500 & 45.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The ligaments characteristics adopted in the model: \(\varepsilon_{ref}\) and \(L_{ref}\) are respectively the strain derived from [26] and the ligament length in our reference position (straight knee); \(L_{0}\) is the rest length of the ligament; \(K\) is the stiffness (\(=F/\varepsilon\)) in the linear portion of the ligament characteristics; \(\Delta L\) and \(F_{ref}\) are, respectively, the elongation and the ligament tension in the reference position. ACL- Anterior Cruciate Ligament, PCL: Posterior Cruciate Ligament (a: anterior bundle, p: posterior bundle); LCL: Lateral Collateral Ligament (1,2,3: anterior, middle, posterior component respectively); MCL: Medial Collateral Ligament (a: anterior, i: intermediate, p: posterior, da: deep anterior; dp: deep posterior components); CAP: Capsular Ligament (Ant-L: anterolateral; Post-L: posterolateral; Post-M: posteromedial components). the ligament. This occurred for LCL and posterior capsule. The stiffness values are reported in the sixth column of Table 1. The resulting pre-tensions of the ligaments in the reference position are reported in the last column. These forces ranged from 0 (slack ligaments: PCL-a, MCL-da) and 45 N (posterior capsule: CAP-Post-L and CAP-Post-M).