## 2 Materials and Methods
### Results from Estimating Muscle Torque Using the GA  
The results from validating the second trial are shown in Figure 11. Here, the values denote the calculated joint torque and estimated torque, representing the sum of muscle torque for the rectus abdominis and erector spinae using the GA. The associated model parameters and calculated _RMSE_ for the training data and the validation session are shown in the Table 3. It is unsatisfactory that the results of muscle torque from the training session and validation session are different in each trial because this means that the results differ depending on the choice of training data. As shown in Table 2, the _RMSE_ results for the training data and the validation session were consistently similar in every trial with the proposal method. Regarding the delay of the timing of peak in the result of estimating muscle torque using the GA in comparison to \(\tau_{at}\) as shown in Figure 11, the similar activation of back muscles after maximum bending was observed in previous research [32]. Hence, the result might represent the actual muscle activation. From these results, the model and the parameters obtained using the GA are suitable for predicting the muscle torque in co-contracted activations of the rectus abdominis and erector spinae. As an example of estimating muscle torque in the rectus abdominis and erector spinae using these associated model parameters as shown in Figure 12, there were 18.62 N and 233.2 N of respective torque at 5.25 s into Trial 2. From these results, the rectus abdominis was estimated to generate about 8.0% of the torque generated by the erector spinae, although this value was estimated at almost zero with the musculoskeletal model that did not consider co-contraction activation of agonist and antagonist muscles. The activation of the rectus abdominis is responsible for flexing the lumbar spine, and it is instrumental in increasing joint stabilization. In fact, the muscle torque generated by the erector spinae was 223.2 N according to the musculoskeletal model. That is, this value is lower than that from the GA-optimized model at 5.25 s into Trial 2 in this study. Therefore, the muscle stress is thought to be higher than when the antagonist muscle is not activated. This mechanism cannot be overlooked when managing LPP during pregnancy. Indeed, the GA-optimized model provides important information. It is said that the weight gain and downward shift to the center of gravity in the forward direction during pregnancy increases muscle activation especially in back muscles, accumulating muscle stress that causes LPP. Moreover, less trunk stability from changes to the body structure can lead to co-contraction activations of the abdominal and back muscles to compensate for these changes. According to the results of this study, using the GA, co-contraction activation was observed as expected. Although the activation of agonist and antagonist muscles is useful to enhance trunk stability, it concurrently increases the muscle load of the back muscles. Thus, this activation is a notable point for managing LPP during pregnancy. The muscle activation and muscle torque of the trunk muscles of pregnant women can thus be accurately estimated using the method proposed in this study. In addition, the proposed  
Figure 11: Results from estimating muscle torque using the GA in Trial 2. Figure 10: Results from estimating the muscle torque of the rectus abdominis and erector spinae with the musculoskeletal model. method does not require measuring MVC tasks that are dangerous for pregnant women to perform. Therefore, the proposed method provides an effective and safe way to manage LPP during pregnancy. There were several limitations in the current study. First, the study used data from one person, rather than many participants. Therefore, further research is needed to investigate the versatility of the relationships observed in the study. Moreover, the model was made for Japanese women because the participant was Japanese.