# Validation of Lumbar Compressive Force Simulation in Forward Flexion Condition
## 4 Discussion
The geometry of trunk muscles including erector spinae (ES), quadratus lumborum (QL), pasos (PA), internal oblique (IO), external oblique (EO), rectus abdominis (RA), and latissimus dorsi (LA) has been reported by [PERSON], [PERSON], and [PERSON] [48; 49; 50]. [PERSON] estimated the relative displacement between L4/L5 level and the muscles' endpoints [48]. [PERSON] presented the L4/L5 but each level from the rib cage to the sacrum and described a more detailed model for multifidus and erector spinae [49]. [PERSON] presented a more detailed model of EO and IO than [PERSON] [50]. However, the pattern of the muscle recruitment varies among people in lateral flexion and twisting. It is necessary to obtain \begin{table}
\begin{tabular}{c c c} \hline \hline
**Researcher** & **Subjects** & **Length (cm)** \\ \hline [PERSON] [45] & 13 & 8.5 (0.68) \\ \hline [PERSON] [44] & 8 males, 5 females & 6.00 (0.37), 5.85 (0.49) \\ \hline [PERSON] [46] & 11 males, 10 females & 7.1 \(\pm\) 2, 6.5 \(\pm\) 2 \\ \hline [PERSON] [47] & 4 males & 5.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Back muscle’s moment arm estimated by previous studies. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Researchers** & **Characteristic** & **Lumbar Disc Level** & **IDP (_MPa_)** & **Load (N)** \\ \hline \multirow{3}{*}{[PERSON] [39]} & 22 subjects & L4/L5 & 0.74 (standing upright) & \multirow{3}{*}{1000} \\  & 19–96 years old & L5/S1 & 0.73 (standing upright) & & \\ \cline{1-1}  & 174 cm & & & \\ \hline \multirow{3}{*}{[PERSON] [40]} & 6 subjects & L4/L5 & 0.84 (standing upright) & \multirow{3}{*}{100–750} \\  & 49.5 (33–66) years old & L5/S1 & 0.78 (standing upright) & & \\ \cline{1-1}  & & & 0.99 (20\({}^{\circ}\) flexion) & & \\ \cline{1-1}  & & & 0.97 (20\({}^{\circ}\) flexion) & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of \(IDP\) at L4/L5 and L5/S1. how the muscles quantitatively affect in lateral flexion and twisting, as it has been found in forward flexion where erector spinae is the major muscle and the moment arm can be considered as a constant. Even though the representative moment arm is difficult to use aside from forward flexion, it is possible to establish the relationship between the CF and the dominant factors, such as flexion angle, twisting angle, and the external load based on the regression analysis. Therefore, the performance of this model in lateral flexion and twisting motion remains to be investigated in the future. Our experiments were conducted in a 2D plane, which cannot represent realistic movement performed during caregiving tasks. We consider, however, that the forward flexion motions can represent actual caregiving transfer task motions. The critical issue is whether the CF estimated in 3D caregiving motions is similar to that obtained from a 2D model. [PERSON] reported that, in manual material transfer tasks, there is a minor L5/S1 moment difference between 2D and 3D tasks for the asymmetric handling task with the angle ranging from 0\({}^{\circ}\) to 90\({}^{\circ}\)[20]. Considering [PERSON]'s data, if the erector spinae's moment arm is taken as 5.3 cm, as proposed by [PERSON] et al. (2006), the error in the CF at 10\({}^{\circ}\), 30\({}^{\circ}\), 60\({}^{\circ}\), and 90\({}^{\circ}\) of CF at 0\({}^{\circ}\) is 1.7%, 1.7%, 0%, and 1.3%, respectively [20]. These errors imply that transfer motions can be simplified by 2D flexion when taking CF as the safety assessment standard. By studying 2D flexion, we can estimate the peak CF achieved during caregiving tasks. In this study, we assume that CF is one of the major factors contributing to back pain and the CF should be similar at the same flexion angle in symmetric forward flexion and extension process. The second assumption is supported by [PERSON]'s invasive data [51]. However, extension could result in back pain not because of the lumbar but instead the hip: in the flexion-extension process, LBP patients are more likely to have an increase in gluteal fatigability related to LBP in extension than healthy people [52].