# Are Torque-Driven Simulation Models of Human Movement Limited by an Assumption of Monoarticularity?
## 2 Methods
### Model Evaluation
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Segment**} & \multirow{2}{*}{**Length**} & \multirow{2}{*}{**Mass**} & \multirow{2}{*}{**Mass Centre Location**} & \multirow{2}{*}{**MOI**} \\ \cline{2-2} \cline{5-5}  & & **[m]** & **[kg]** & **[m]** & **[kg\(\cdot\)m\({}^{2}\)]** \\ \hline shank & 0.408 & 8.439 & 0.175 & 0.1054 \\ thigh & 0.406 & 21.577 & 0.171 & 0.3049 \\ trunk & 0.558 & 31.732 & 0.287 & 1.0231 \\ head & 0.339 & 7.075 & 0.172 & 0.0624 \\ upper arm & 0.275 & 5.345 & 0.12 & 0.0362 \\ forearm and hand & 0.408 & 3.21 & 0.148 & 0.0365 \\ \hline \hline \end{tabular} Note: Mass centre location relative to the proximal joint, MOI about the transverse axis through the mass centre.  
\end{table} 
Table 3: Inertia parameters for each segment in the models SJ and TJ. the participant). Including this measure of rotation in flight within the matching process ensured that matching simulations had an appropriate amount of rotation in flight. \[\sqrt{\frac{\left(\Delta\theta_{\mathbf{M}}^{2}+\Delta\theta_{A}^{2}+\Delta\theta_{ \mathbf{K}}^{2}+\Delta\theta_{\mathbf{H}}^{2}+\Delta\theta_{\mathbf{S}}^{2}+\Delta\theta_{ \mathbf{0}}^{2}+\Delta\R^{2}\right)}{7}} \tag{4}\]  
where \(\mathbf{\Delta\theta_{M}}\), \(\mathbf{\Delta\theta_{A}}\), \(\mathbf{\Delta\theta_{K}}\), \(\mathbf{\Delta\theta_{H}}\), \(\mathbf{\Delta\theta_{S}}\), \(\mathbf{\Delta\theta_{\theta}}\) are defined in Equation (3) and \(\mathbf{\Delta R}\) represents the RMS difference between measured and simulated net vertical ground reaction force expressed as a percentage of the peak measured force for this phase of the simulation. To obtain a matching simulation, a genetic algorithm [39] was used to vary the parameters defining the activation of each torque generator in the model between physiologically realistic bounds to minimise the objective difference function. The squat jump and ascent phase of countermovement jump required a single ramp function (four activation parameters per torque generator (the time at initiation of the final ramp, P\({}_{0}\); one ramp duration, TR\({}_{3}\); and two activation levels between which the function ramps, A\({}_{2}\), A\({}_{3}\); Figure 2)). For the countermovement descent, phase a more complex ramp function was required (three ramps consisting of 10 activation parameters per torque generator (the time at initiation of the final ramp, P\({}_{0}\); intervals between consecutive ramps at which activation is constant, P\({}_{1}\), P\({}_{2}\); three ramp durations, TR\({}_{1}\), TR\({}_{2}\), TR\({}_{3}\); and four activation levels between which the function ramps, A\({}_{0}\), A\({}_{1}\), A\({}_{2}\), A\({}_{3}\))). As well as the activation parameters, an additional 12 parameters were varied for the squat jump and ascent phase of the countermovement jump: The torsional spring stiffness, dampening and natural angle (equivalent to natural length in a linear spring) at the MTP joint, the strain of the series elastic component for each torque generator at peak isometric torque and the trunk angular velocity (by 1% from the experimental values). For the descent phase of the countermovement jump, the initial trunk angular velocity was also allowed to vary (by 1% from the experimental values) with the other 11 parameters fixed from the values obtained for the ascent phase of the jump. This resulted in the following number of parameters being varied for each activity/model: Squat jump (48 parameters (9 \(\times\) 4 + 12) for S) and 60 parameters (12 \(\times\) 4 + 12) for TJ), countermovement descent phase (91 parameters (9 \(\times\) 10 + 1) for SJ and 121 parameters (12 \(\times\) 10 + 1) for TJ), countermovement ascent phase (48 parameters (9 \(\times\) 4 + 12) for SJ and 60 parameters (12 \(\times\) 4 + 12) for TJ).