## 2 Materials and Methods
### Estimating Co-Contraction Activation Using a GA  
From a comparison between the results of the musculoskeletal model and EMG, it is observed that the co-contraction activation of agonist and antagonist muscles cannot be estimated with the current system. Thus, other estimation methods of the muscle torque of the rectus abdominis and erector spinae for pregnant women were needed to resolve the problem. However, most proposed methods for estimating muscle torque require measuring MVC tasks and the MVC of a rectus abdominis is risky during pregnancy. Consequently, an estimation method for the muscle torque and joint torque from EMG using a GA was selected [21]. With this method, some conversion models used to calculate torque from EMG data were proposed. From these models, the model shown in Equation (2) was used as a reference in this study:  
\[\tau_{{}_{est}}=x_{i}E_{i}^{x_{i}}+x_{j}E_{i}^{x_{i}}, \tag{2}\]  
\(\tau_{{}_{est}}=\) estimated torque, \(E_{i}=\) processed EMG signal, \(x_{i}=\) associated model parameters.  
Equation (2) expresses the formula for estimating joint torque \(\tau_{{}_{est}}\) generated in the joint from the joint-bridging muscle, obtained from the EMG signal \(E_{i}\). Here, \(\tau_{{}_{est}}\) indicates the muscle torque used for the motion of the joint. The purpose of this study was to estimate two muscles torques. That is to say, the EMG signal of the rectus abdominis and erector spinae were used to estimate the joint torque generated from these muscles. Owing to this, \(E_{{}_{EA}}\) and \(E_{{}_{LO}}\) denote EMG data for the rectus abdominis and erector spinae, respectively, and these were substituted for \(E_{i}\) in Equation (2). Therefore, Equation (3) was used in this study, where \(k\) denotes the sampling time:  
\[\tau_{{}_{est}}=\tau_{{}_{est},{}_{EA}(k)}+\tau_{{}_{est},{}_{LO}(k)}, \tag{3}\] \[\tau_{{}_{est},{}_{EA}(k)}=x_{i}E_{{}_{EA}(k)}^{x_{i}}+x_{j}E_{{}_ {EA}(k)}^{x_{i}},\] \[\tau_{{}_{EL},{}_{LO}(k)}=x_{j}E_{{}_{LO}(k)}^{x_{i}}+x_{j}E_{{}_ {LO}(k)}^{x_{i}},\]  
\(E_{{}_{EA}}=\) processed EMG signal of rectus abdominis, \(E_{{}_{LO}}=\) processed EMG signal of Longissimus.  
A system overview of this study is shown in Figure 7. The joint torque during STS motions was calculated for the musculoskeletal model using the skeletal data, motion data, and force data by inverse dynamics calculation. Thus, this joint torque is precise by comparison to the estimated muscle torque from the current musculoskeletal model. Meanwhile, torque expressed using Equation (3) from EMG should be equal to the joint torque, and this was used as an input value. From these values, the muscle torque was estimated using an optimized GA using Equation (4). The fitness values (FS) can only be maximized by determining a certain estimated torque (\(\tau_{{}_{est}}\)) that fits the actual torque data (\(\tau_{{}_{est}}\)). In this study, the calculated joint torque from the musculoskeletal model is regarded as the actual torque. Through Equation (4), the optimal associated model parameters (\(x_{j}\)) were estimated using seven datasets for motion analysis from eight trials as learning data. Then, the parameters were validated using EMG data that was not used for learning.  
Figure 6: Coordinate system and definition of angles in the study.  
stress related to LPP, and this is useful for managing LPP [31]. Furthermore, the antagonist activation of the rectus abdominis to the erect spinae as an agonist muscle was not conspicuous from EMG, as shown in Figure 9. For example, the muscle torque of the rectus abdominis as an extension of the trunk when standing up from a chair was estimated at almost zero in the musculoskeletal model, as shown in Figure 10. By contrast, EMG data indicated that the rectus abdominis activated simultaneously with the erect spinae. It is evident from this data that an estimation of the muscle torques from co-contraction activation is needed to understand muscle activation accurately.