## 4 Discussion  
### General  
This study set out to use staged rugby tackle Vicon data to assess the predictive capacity of the MADYMO human body model for head kinematic reconstruction during inertial head loading impacts. The results demonstrated that the predictive capacity was limited in individual cases, with errors \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Ball Carrier**} & \multicolumn{5}{c}{**Change in Resultant Head Linear Velocity (m/s)**} & \multicolumn{5}{c}{**Change in Resultant Head Angular Velocity (rad/s)**} \\ \hline \multirow{3}{*}{**Tackle ID**} & **Closing** & \multirow{3}{*}{**Vicon**} & \multirow{3}{*}{**MADYMO**} & **Difference** & \multirow{3}{*}{**\% Error (\%**} & \multirow{3}{*}{**Vicon**} & **MADYMO** & **MADYMO**- & **\% Error (\%** \\  & **(m/s)** & & & **Vicon**) & & & & **Vicon**) & \\ \hline Upper 2 & 3.95 & 1.49 & 1.38 & \(-0.11\) & \(-7\) & 5.00 & 7.85 & 2.85 & 57 \\ Upper 3 & 4.26 & 0.45 & 1.94 & 1.50 & 336 & 5.79 & 4.48 & \(-1.31\) & \(-23\) \\ Upper 4 & 4.05 & 1.17 & 1.12 & \(-0.05\) & \(-4\) & 6.81 & 5.73 & \(-1.09\) & \(-16\) \\ Upper 5 & 4.38 & 1.33 & 1.27 & \(-0.06\) & \(-4\) & 6.80 & 8.51 & 1.71 & 25 \\ Upper 6 & 4.53 & 2.23 & 2.45 & 0.22 & 10 & 6.11 & 7.43 & 1.32 & 22 \\ Upper 7 & 4.88 & 2.52 & 1.02 & \(-1.50\) & \(-9\) & 10.20 & 8.52 & \(-1.67\) & \(-16\) \\ Upper 8 & 4.54 & 1.43 & 1.57 & 0.14 & 10 & 4.02 & 6.30 & 2.28 & 57 \\ Upper 9 & 5.18 & 2.21 & 1.52 & \(-0.69\) & \(-31\) & 7.64 & 8.63 & 0.99 & 13 \\ Upper 10 & 4.57 & 2.53 & 1.42 & \(-1.11\) & \(-44\) & 9.62 & 6.76 & \(-2.86\) & \(-30\) \\ Upper 11 & 4.00 & 2.68 & 1.44 & \(-1.23\) & \(-46\) & 10.87 & 5.79 & \(-5.08\) & \(-47\) \\ Median & 4.38 & 1.49 & 1.42 & 0.22 & 10 & 6.80 & 6.76 & 1.67 & 23 \\ (Absolute) & 4.03 & 1.25 & 1.20 & 0.09 & 6 & 5.40 & 5.76 & 1.20 & 16 \\
25 th Percentile (Absolute) & 4.56 & 2.38 & 1.55 & 1.17 & 45 & 8.63 & 8.18 & 2.57 & 39 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: _Cont._  
Figure 3: Comparison between the predicted multibody model (MADYMO) and 3D motion laboratory (Vicon) peak ball carrier change in resultant head angular and linear velocity for upper and mid/lower trunk tackles. Each symbol corresponds to a tackle and is matched for both graphs. ranging up to 336% and 366% for the change in resultant head linear and angular velocity, respectively. The reasons for this may include: (1) the model contact and joint stiffness parameters, (2) the model shape and mass distribution and (3) the model player-to-player friction parameters do not realistically reproduce player-to-player impacts in rugby union. The intensity of the staged tackles was significantly lower than during competitive play as the impact speeds of the ball carrier and tackler were around 2-3 times lower than average impact speeds in elite game environments (4.8 m/s and 5.6 m/s, respectively) [30]. This gave relatively low changes in ball carrier head linear and angular velocity in the motion laboratory trials, resulting in high percentage errors for the model predictions, even though the absolute errors could be considered small [1]. Thus, it is possible that the model may be better suited to assessing inertial loading in higher velocity impacts as it has been validated for vehicle-cadaver impacts (usually 40 km/h impacts [1,31]). The unlocked joint condition is also more representative of an unaware standing pedestrian than a trained rugby player bracing for contact. This may explain why the model has previously shown lower errors for head kinematic predictions during vehicle-cadaver collisions (maximum of 36% for head linear velocity predictions at the point of head-windscreen impact [10]). The models generally (with some exceptions) over-predicted peak ball carrier change in resultant head angular velocity but under-predicted peak ball carrier change in resultant head linear velocity. This suggests that the joint restraints torques in the model trunk and neck are too low and future emphasis should be on implementing active musculature in the models.