## 4 Discussion
### Modelling and Validation  
The model used in this study is \"length-controlled\". This means that the shortening of a muscle was set and all other variables such as joint angles, bone segments orientation and forces were obtained as a result. The selected shortening velocity was \(-2\) cm/s and corresponded approximately to an angular velocity of \(20^{\circ}\)/s in dorsiflexion. This value is comparable to the velocity at which voluntary dorsiflexion is performed during selective tests at the bedside [47]. It should be remembered, though, that the choice of this shortening velocity was not intended to replicate a physiologic condition (e.g., the peak of dorsiflexion velocity occurring during walking, which is in the order of \(100^{\circ}\)/s--approximately \(20^{\circ}\) in 0.2 s after foot-off). Our intention was to avoid sharp accelerations and the corresponding inertia forces that would have tainted the muscle contractions, particularly at the beginning of the movement. On the one hand, the shortening velocity adopted is slower than the physiological one required for dorsiflexion during activities such as walking. On the other hand, our model contains neither dampening elements (e.g., capsule, muscle viscosity) nor  
Figure 7: From left to right: progressive dorsiflexion until the SO stops lengthening, and foot inversion occurs associated with plantar flexion of the lateral side of the foot. In this example, SO lengthening was limited to 75%. reflex activations (e.g., spasticity) and so the forces and the resulting movement do not depend on the value of the shortening velocity. Because of the lack of elements sensitive to the dorsiflexion velocity, i.e., muscle viscosity and muscle spasticity, our model does not fully represent the complex biomechanics of ankle dorsiflexion. In this regard, it is reasonable to suppose that phenomena limiting the triceps surae extensibility would lead to deviations similar to those modelled in this study, where TS extensibility was limited at four discrete levels. However, this would require a specific simulation that was out of the scope of our study. In our simulations, muscle forces achieved (210 N for the TA) are all within a range of feasibility. An interesting paper by [PERSON] [48] reports, in a controlled stimulation condition, a range of TA force from 157 +/\(-\) 19 N to 644 +/\(-\) 88 N. Similarly, data reported by [PERSON] [49] show a maximum voluntary dorsiflexion force of approximately 300 N, measured by a force sensor positioned on top of the metatarsal heads. If the lever arm of the force were twice the lever arm of the muscle dorsiflexors as a whole, the dorsiflexion force would be approximately 600 N. No reference data were found for EDL. Still, one can ponder on the relative strength that can be inferred by considering the physiological cross-sectional area (PCSA) of the two muscles. [PERSON] and [PERSON] [50], in a cadaver dissection study, reported a PCSA of 16.88 cm\({}^{2}\) for the TA and 7.46 cm\({}^{2}\) for the EDL, corresponding to 44% of the TA PCSA. The maximum force we obtained for the EDL was 50 N, less than 24% of the TA force. We can thus confirm that even for the EDL, the forces obtained in our simulation were far below the maximum force capacity of this muscle. With regard to the numerical solution stability, it is worth noting that even dramatically altering the muscle forces (the alternative removal of the TA or EDL, different limitations of the SO length excursion), the software was able to proceed in the simulations and compute the corresponding changes in foot movements. Of course, an overall assessment of the accuracy of the results was impossible since it is impossible to obtain a controlled contraction of one single muscle in a real individual. Consequently, we were unable to obtain any real reference data.