# Validation of Lumbar Compressive Force Simulation in Forward Flexion Condition
## 4 Discussion
In our study, we aim to validate the CF simulator for standardization of lumbar safety. Although the hip muscle is related to LBP, this factor cannot be quantitatively evaluated for LBP currently. We emphasize that compressive force is suitable for standardization. For each sample, the values along the horizontal axis in Figure 7a-c were obtained from different flexion postures in the invasive experiment, and the values in the vertical axis were obtained by each model under the same conditions. The linear relationship helps to understand whether the estimated data are in good agreement with the experimental data. In Figure 7d, the difference between the models is presented by the distance (D) between the marker and the line y = x shown in Figure 7a-c. It can be seen that the CFs estimated using the Kruskal-Wallis test on the D of the Merryweather, Potvin, and CF simulator are significantly different (\(p\leq 0.001\)). In Table 4, the slope implies that both the CF simulator and the model by [PERSON] perform better than the model by [PERSON]. Thus, we conclude that dynamic models can obtain more accurate CF estimates at L5/S1 than static ones. The discrepancy between the model of [PERSON] and the invasive measurements is probably due to the difference in the CF during static and dynamic motion. The Kruskal-Wallis test results show a significant difference (\(p\leq 0.01\)) among the estimates of the models and the invasive data. The Mann-Whitney test is performed between the estimated CF by each model and the invasive data, respectively. Considering the small amount of invasive data available, the significance level of invasive data and estimated CF by each model is set as \(\alpha\) = 0.01. [PERSON]'s data show a highly significant difference with the invasive data in both 0\({}^{\circ}\) and 30\({}^{\circ}\) flexion conditions. A small difference is observed between the CF simulator and the [PERSON]'s model. Even though the anthropometric data vary, the CF estimated with the simulator and Merryweather model have a smaller difference from the invasive measurement than the estimates of [PERSON]'s model. However, in the 3D condition, [PERSON]'s model cannot estimate the external forces other than those exerted by the hands. During caregiving tasks performed with arms, which shorten the moment arm of external loads, [PERSON]'s model can overestimate the moment at L5/S1. Under this condition, the CF simulator can estimate the external force acting on any point of the body. Because the back muscle model can also be used in 3D cases, the simulator can be applied in various caregiving conditions. None of the previous studies quantitatively evaluated the precision of a model by using invasive data [17; 23]. An important reason is that invasive data are reported in only a few conditions and the subjects are limited. Thus, we compared only 0 and 30\({}^{\circ}\) conditions between invasive data and estimated data, where most of the invasive data are reported. Although the consistency between [PERSON]'s model and invasive measurement is moderate, it is promised expected to promote the reliability if more invasive data are reported in the future. Even so, not all simulators can reconstruct the motion and simulate the conditions while relying only on the reported data of invasive experimental conditions. A simpler \"precision evaluating model\" is taken as the bridge between invasive measurement and some complex model, such as the CF simulator; if the precision of the precision evaluating model is accepted, a complex model in good or excellent consistency with the precision evaluating model is also accepted.